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Viscoelasticità - Wikipedia
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mw-first-heading"><span class="mw-page-title-main">Viscoelasticità</span></h1> <div class="tagline"> tipo di modello matematico </div> </div> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"><a role="button" href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#p-lang" data-mw="interface" data-event-name="menu.languages" title="Lingua" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet language-selector"> <span class="minerva-icon minerva-icon--language"></span> <span>Lingua</span> </a></li> <li id="page-actions-watch" class="page-actions-menu__list-item"><a role="button" id="ca-watch" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Speciale:Entra&returnto=Viscoelasticit%C3%A0&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.watch" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet menu__item--page-actions-watch"> <span class="minerva-icon minerva-icon--star"></span> <span>Segui</span> </a></li> <li id="page-actions-edit" class="page-actions-menu__list-item"><a role="button" id="ca-edit" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> <span class="minerva-icon minerva-icon--edit"></span> <span>Modifica</span> </a></li> </ul> </nav><!-- version 1.0.2 (change every time you update a partial) --> <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"> <script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script> <div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"> <section class="mf-section-0" id="mf-section-0"> <p>La <b>viscoelasticità</b> è un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Modello_matematico?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modello matematico">modello matematico</a> che descrive un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Materiale?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Materiale">materiale</a> che si comporta in modo intermedio tra un <i>solido <a href="https://it-m-wikipedia-org.translate.goog/wiki/Elasticit%C3%A0_(meccanica)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Elasticità (meccanica)">elastico</a></i> e un <i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Fluido?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Fluido">fluido</a></i>. Costituisce un modello ampiamente studiato in <a href="https://it-m-wikipedia-org.translate.goog/wiki/Reologia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Reologia">reologia</a>. Uno dei modelli più semplici di materiale viscoelastico è il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Fluido_alla_Boger?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Fluido alla Boger">fluido alla Boger</a>, in cui la viscosità è costante.</p> <p>L'individuazione del comportamento viscoelastico viene svolta misurando la variazione della <a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscosit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Viscosità">viscosità</a> η in funzione della velocità di deformazione <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\gamma }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> γ<!-- γ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\dot {\gamma }}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c250a2cd0b68db26e9663686345f6cee8074d5f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.676ex;" alt="{\displaystyle {\dot {\gamma }}}"></span>. Nel caso di un fluido viscoelastico la viscosità dipende sia dalla temperatura che dalla velocità di deformazione, mentre per un fluido puramente viscoso la viscosità dipende esclusivamente dalla temperatura.</p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="it" dir="ltr"> <h2 id="mw-toc-heading">Indice</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Storia"><span class="tocnumber">1</span> <span class="toctext">Storia</span></a></li> <li class="toclevel-1 tocsection-2"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Definizione"><span class="tocnumber">2</span> <span class="toctext">Definizione</span></a> <ul> <li class="toclevel-2 tocsection-3"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Esempi_di_materiali_viscoelastici"><span class="tocnumber">2.1</span> <span class="toctext">Esempi di materiali viscoelastici</span></a></li> </ul></li> <li class="toclevel-1 tocsection-4"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Comportamento_reologico_dei_materiali_viscoelastici"><span class="tocnumber">3</span> <span class="toctext">Comportamento reologico dei materiali viscoelastici</span></a></li> <li class="toclevel-1 tocsection-5"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modulo_di_rilassamento"><span class="tocnumber">4</span> <span class="toctext">Modulo di rilassamento</span></a></li> <li class="toclevel-1 tocsection-6"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modulo_dinamico"><span class="tocnumber">5</span> <span class="toctext">Modulo dinamico</span></a></li> <li class="toclevel-1 tocsection-7"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Viscoelasticit%C3%A0_lineare_e_non_lineare"><span class="tocnumber">6</span> <span class="toctext">Viscoelasticità lineare e non lineare</span></a></li> <li class="toclevel-1 tocsection-8"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Equazioni_costitutive_dei_materiali_viscoelastici"><span class="tocnumber">7</span> <span class="toctext">Equazioni costitutive dei materiali viscoelastici</span></a> <ul> <li class="toclevel-2 tocsection-9"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modelli_a_2_elementi"><span class="tocnumber">7.1</span> <span class="toctext">Modelli a 2 elementi</span></a> <ul> <li class="toclevel-3 tocsection-10"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_di_Maxwell"><span class="tocnumber">7.1.1</span> <span class="toctext">Modello di Maxwell</span></a></li> <li class="toclevel-3 tocsection-11"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_di_Kelvin-Voigt"><span class="tocnumber">7.1.2</span> <span class="toctext">Modello di Kelvin-Voigt</span></a></li> </ul></li> <li class="toclevel-2 tocsection-12"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modelli_a_3_elementi"><span class="tocnumber">7.2</span> <span class="toctext">Modelli a 3 elementi</span></a> <ul> <li class="toclevel-3 tocsection-13"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_lineare_standard_di_Zener"><span class="tocnumber">7.2.1</span> <span class="toctext">Modello lineare standard di Zener</span></a></li> <li class="toclevel-3 tocsection-14"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_di_Jeffreys-Lethersich"><span class="tocnumber">7.2.2</span> <span class="toctext">Modello di Jeffreys-Lethersich</span></a></li> </ul></li> <li class="toclevel-2 tocsection-15"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_a_4_elementi_di_Alfrey-Burgers"><span class="tocnumber">7.3</span> <span class="toctext">Modello a 4 elementi di Alfrey-Burgers</span></a></li> <li class="toclevel-2 tocsection-16"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modelli_Multi-elemento"><span class="tocnumber">7.4</span> <span class="toctext">Modelli Multi-elemento</span></a> <ul> <li class="toclevel-3 tocsection-17"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_di_Maxwell-Weichert"><span class="tocnumber">7.4.1</span> <span class="toctext">Modello di Maxwell-Weichert</span></a></li> <li class="toclevel-3 tocsection-18"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Modello_di_Kelvin-Voigt-Weichert"><span class="tocnumber">7.4.2</span> <span class="toctext">Modello di Kelvin-Voigt-Weichert</span></a></li> </ul></li> </ul></li> <li class="toclevel-1 tocsection-19"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Rilassamento_viscoelastico"><span class="tocnumber">8</span> <span class="toctext">Rilassamento viscoelastico</span></a></li> <li class="toclevel-1 tocsection-20"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Note"><span class="tocnumber">9</span> <span class="toctext">Note</span></a></li> <li class="toclevel-1 tocsection-21"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Bibliografia"><span class="tocnumber">10</span> <span class="toctext">Bibliografia</span></a></li> <li class="toclevel-1 tocsection-22"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Voci_correlate"><span class="tocnumber">11</span> <span class="toctext">Voci correlate</span></a></li> <li class="toclevel-1 tocsection-23"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Altri_progetti"><span class="tocnumber">12</span> <span class="toctext">Altri progetti</span></a></li> <li class="toclevel-1 tocsection-24"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Collegamenti_esterni"><span class="tocnumber">13</span> <span class="toctext">Collegamenti esterni</span></a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Storia">Storia</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Storia" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Nel <a href="https://it-m-wikipedia-org.translate.goog/wiki/XIX_secolo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="XIX secolo">XIX secolo</a>, i fisici <a href="https://it-m-wikipedia-org.translate.goog/wiki/James_Clerk_Maxwell?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="James Clerk Maxwell">James Clerk Maxwell</a>, <a href="https://it-m-wikipedia-org.translate.goog/wiki/Ludwig_Boltzmann?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ludwig Boltzmann">Ludwig Boltzmann</a>, <a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Woldemar_Voigt&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Woldemar Voigt (la pagina non esiste)">Woldemar Voigt</a> e <a href="https://it-m-wikipedia-org.translate.goog/wiki/William_Thomson,_I_barone_Kelvin?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="William Thomson, I barone Kelvin">William Thomson Kelvin</a> studiarono i fenomeni di <a href="https://it-m-wikipedia-org.translate.goog/wiki/Scorrimento_viscoso?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Scorrimento viscoso">scorrimento viscoso</a> (anche detto <i>"creep"</i>) e recupero di vari materiali, tra cui: <a href="https://it-m-wikipedia-org.translate.goog/wiki/Vetro?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Vetro">vetro</a>, <a href="https://it-m-wikipedia-org.translate.goog/wiki/Metallo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Metallo">metalli</a> e <a href="https://it-m-wikipedia-org.translate.goog/wiki/Gomma?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gomma">gomme</a>.<sup id="cite_ref-McCrum_1-0" class="reference"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-McCrum-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Il modello della viscoelasticità fu ulteriormente elaborato alla fine del <a href="https://it-m-wikipedia-org.translate.goog/wiki/XX_secolo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="XX secolo">XX secolo</a> in occasione della sintesi dei primi <a href="https://it-m-wikipedia-org.translate.goog/wiki/Polimeri?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Polimeri">polimeri</a> sintetici,<sup id="cite_ref-McCrum_1-1" class="reference"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-McCrum-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> che manifestano comportamento viscoelastico.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Definizione">Definizione</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Definizione" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <p>I materiali puramente viscosi rispondono ad una <a href="https://it-m-wikipedia-org.translate.goog/wiki/Azione_esterna?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Azione esterna">sollecitazione</a> tangenziale manifestando un comportamento coerente con la <a href="https://it-m-wikipedia-org.translate.goog/wiki/Legge_di_Newton-Stokes?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Legge di Newton-Stokes">legge di Newton</a>, cioè originando al loro interno uno <a href="https://it-m-wikipedia-org.translate.goog/wiki/Sforzo_tangenziale?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sforzo tangenziale">sforzo tangenziale</a> pari al prodotto della <a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Velocit%C3%A0_di_deformazione&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Velocità di deformazione (la pagina non esiste)">velocità di deformazione</a> e della viscosità; se sono invece sottoposti ad una sollecitazione normale non si oppongono in alcun modo.</p> <p>I materiali elastici rispondono ad una sollecitazione normale manifestando un comportamento coerente con la <a href="https://it-m-wikipedia-org.translate.goog/wiki/Legge_di_Hooke?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Legge di Hooke">legge di Hooke</a>, cioè originando al loro interno uno <a href="https://it-m-wikipedia-org.translate.goog/wiki/Sforzo_normale?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sforzo normale">sforzo normale</a> pari al prodotto del <a href="https://it-m-wikipedia-org.translate.goog/wiki/Modulo_di_Young?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Modulo di Young">modulo di Young</a> e della deformazione (espressa in termini di <a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Allungamento_percentuale&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Allungamento percentuale (la pagina non esiste)">allungamento percentuale</a>) e ritornando al loro stato originario quando queste sollecitazioni cessano; se sono invece sottoposti ad una sollecitazione tangenziale non si oppongono in alcun modo.</p> <p>I materiali viscoelastici si oppongono sia alle sollecitazioni tangenziali sia alle sollecitazioni normali, generando quindi al loro interno sia sforzi tangenziali sia sforzi normali.</p> <div class="mw-heading mw-heading3"> <h3 id="Esempi_di_materiali_viscoelastici">Esempi di materiali viscoelastici</h3><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Esempi di materiali viscoelastici" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <p>Sebbene alcuni materiali seguano abbastanza bene la legge di Newton oppure la legge di Hooke, tutti i materiali mostrano una deviazione più o meno marcata dal comportamento elastico e dal comportamento puramente viscoso, per cui dal punto di vista pratico tutti i materiali sono viscoelastici.</p> <p>Di solito i metalli e le leghe (quali ad esempio l'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Acciaio?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Acciaio">acciaio</a> o l'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Alluminio?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Alluminio">alluminio</a>) e il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Quarzo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Quarzo">quarzo</a> (a <a href="https://it-m-wikipedia-org.translate.goog/wiki/Temperatura_ambiente?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Temperatura ambiente">temperatura ambiente</a> e per piccole deformazioni) hanno un comportamento pressoché elastico. I polimeri sintetici, il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Legno?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Legno">legno</a>, i tessuti umani e i metalli ad alta temperatura mostrano invece effetti viscoelastici significativi.</p> <p>Alcuni esempi di materiali viscoelastici includono: polimeri amorfi, polimeri semicristallini, biopolimeri, metalli ad elevate temperature, e materiali bituminosi.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Comportamento_reologico_dei_materiali_viscoelastici">Comportamento reologico dei materiali viscoelastici</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Comportamento reologico dei materiali viscoelastici" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <p>Nel caso dei materiali viscoelastici, la viscosità, intesa come costante di proporzionalità tra sforzo e velocità di deformazione, dipende dalla velocità di deformazione e quindi dal tempo.</p> <p>La viscosità di un materiale viscoelastico è costituita da due contributi:</p> <ul> <li>la viscosità propriamente detta (in inglese <i>shear viscosity</i>), che è il rapporto tra gli <a href="https://it-m-wikipedia-org.translate.goog/wiki/Sforzi_tangenziali?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sforzi tangenziali">sforzi tangenziali</a> e la velocità di deformazione;</li> <li>la <a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscosit%C3%A0_elongazionale&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Viscosità elongazionale (la pagina non esiste)">viscosità elongazionale</a> (in inglese <i>extensional viscosity</i> o <i>elongational viscosity</i>), che è il rapporto tra gli <a href="https://it-m-wikipedia-org.translate.goog/wiki/Sforzi_normali?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sforzi normali">sforzi normali</a> e la velocità di deformazione.</li> </ul> <p>Alcune proprietà dei materiali viscoelastici sono le seguenti:</p> <ul> <li>se lo sforzo si mantiene costante, la deformazione cresce con il tempo; tale fenomeno è detto "<a href="https://it-m-wikipedia-org.translate.goog/wiki/Scorrimento_viscoso?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Scorrimento viscoso">scorrimento viscoso</a>" (o <i>creep</i>);</li> <li>se si mantiene costante la deformazione, lo sforzo decresce con il tempo; tale fenomeno è detto "<a href="https://it-m-wikipedia-org.translate.goog/wiki/Rilassamento_degli_sforzi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rilassamento degli sforzi">rilassamento degli sforzi</a>";</li> <li>la rigidità del materiale dipende dalla velocità di applicazione del carico;</li> <li>se viene applicato un carico ciclico, avviene un'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Isteresi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Isteresi">isteresi</a> (un ritardo periodico), con conseguente dissipazione (sotto forma di <a href="https://it-m-wikipedia-org.translate.goog/wiki/Calore?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Calore">calore</a>) di <a href="https://it-m-wikipedia-org.translate.goog/wiki/Energia_meccanica?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Energia meccanica">energia meccanica</a>; rappresentando il ciclo di carico in un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Diagramma_sforzo-deformazione?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Diagramma sforzo-deformazione">diagramma sforzo-deformazione</a>, la perdita di energia meccanica è pari all'area del percorso che rappresenta il ciclo di carico;<sup id="cite_ref-Meyers_2-0" class="reference"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Meyers-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> tale perdita di energia meccanica non avviene invece nei materiali elastici, i quali riassumono la loro forma originaria una volta che il carico è rimosso;<sup id="cite_ref-Meyers_2-1" class="reference"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Meyers-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li><style data-mw-deduplicate="TemplateStyles:r140554517">.mw-parser-output .chiarimento{background:#ffeaea;color:#444444}.mw-parser-output .chiarimento-apice{color:#EE0700}@media screen{html.skin-theme-clientpref-night .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-night .mw-parser-output .chiarimento-apice{color:#b32424}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-os .mw-parser-output .chiarimento-apice{color:#b32424}}</style><span class="chiarimento">le onde acustiche (così come quelle vibrazionali) subiscono un'attenuazione, a causa della dissipazione di energia dovuta all'isteresi dei cicli di carico-scarico;</span><sup class="noprint chiarimento-apice">[<i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Aiuto:Chiarezza?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Aiuto:Chiarezza">non chiaro</a></i>]</sup></li> <li>la velocità di rimbalzo di un oggetto in seguito ad un urto con un materiale viscoelastico è inferiore alla velocità dell'oggetto prima dell'urto;</li> <li>durante il rotolamento di un materiale viscoelastico, gli effetti dell'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Attrito_volvente?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Attrito volvente">attrito volvente</a> sono accompagnati da effetti di <a href="https://it-m-wikipedia-org.translate.goog/wiki/Attrito_radente?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Attrito radente">attrito radente</a>.</li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Modulo_di_rilassamento">Modulo di rilassamento</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modulo di rilassamento" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-4 collapsible-block" id="mf-section-4"> <style data-mw-deduplicate="TemplateStyles:r130657691">body:not(.skin-minerva) .mw-parser-output .vedi-anche{font-size:95%}</style> <style data-mw-deduplicate="TemplateStyles:r139142988">.mw-parser-output .hatnote-content{align-items:center;display:flex}.mw-parser-output .hatnote-icon{flex-shrink:0}.mw-parser-output .hatnote-icon img{display:flex}.mw-parser-output .hatnote-text{font-style:italic}body:not(.skin-minerva) .mw-parser-output .hatnote{border:1px solid #CCC;display:flex;margin:.5em 0;padding:.2em .5em}body:not(.skin-minerva) .mw-parser-output .hatnote-text{padding-left:.5em}body.skin-minerva .mw-parser-output .hatnote-icon{padding-right:8px}body.skin-minerva .mw-parser-output .hatnote-icon img{height:auto;width:16px}body.skin--responsive .mw-parser-output .hatnote a.new{color:#d73333}body.skin--responsive .mw-parser-output .hatnote a.new:visited{color:#a55858}</style> <div class="hatnote noprint vedi-anche"> <div class="hatnote-content"> <span class="noviewer hatnote-icon" typeof="mw:File"><span> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" decoding="async" width="18" height="18" class="mw-file-element" data-file-width="286" data-file-height="280"> </noscript><span class="lazy-image-placeholder" style="width: 18px;height: 18px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" data-width="18" data-height="18" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/27px-Magnifying_glass_icon_mgx2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/36px-Magnifying_glass_icon_mgx2.svg.png 2x" data-class="mw-file-element"> </span></span></span> <span class="hatnote-text">Lo stesso argomento in dettaglio: <b><a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Modulo_di_rilassamento&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Modulo di rilassamento (la pagina non esiste)">Modulo di rilassamento</a></b>.</span> </div> </div> <style data-mw-deduplicate="TemplateStyles:r139255918">.mw-parser-output .avviso-mini{border:1px solid #aaa;background-color:#fbfbfb;margin-bottom:.5em;padding:0 2px 0 3px;margin:5px 10%;font-size:90%}.mw-parser-output .avviso-mini>div:first-of-type{margin:2px 2px 2px 0}.mw-parser-output .avviso-mini .mw-collapsible-content{padding:2px 0 0 7px}.mw-parser-output .avviso-mini-informazioni{border-left:10px solid #1e90ff}.mw-parser-output .avviso-mini-contenuto{border-left:10px solid #f28500}.mw-parser-output .avviso-mini-stile{border-left:10px solid #f4c430}.mw-parser-output .avviso-mini-statico{border-left:10px solid limegreen}.mw-parser-output .avviso-mini-struttura{border-left:10px solid #9932cc}.mw-parser-output .avviso-mini-generico{border-left:10px solid #bba}body.skin-minerva .mw-parser-output .avviso-mini{border:none;margin-bottom:1px;padding:inherit}body.skin-minerva .mw-parser-output .avviso-mini .mbox-text-div{font-style:normal}html.client-js body.skin-minerva .mw-parser-output .avviso-mini>div{padding:8px 8px 8px 32px!important;position:relative}</style> <div class="ambox avviso-mini noprint metadata avviso-mini-informazioni plainlinks"> <div class="mbox-text"> <div class="mbox-text-div" style="display:flex; flex-direction:row; align-items:center; column-gap:5px;"> <span style="width:100%"><b>Questa sezione sull'argomento fisica è ancora vuota</b>. <a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/w/index.php?title%3DViscoelasticit%25C3%25A0%26action%3Dedit">Aiutaci</a> a scriverla!</span> </div> </div> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Modulo_dinamico">Modulo dinamico</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=6&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modulo dinamico" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-5 collapsible-block" id="mf-section-5"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r130657691"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139142988"> <div class="hatnote noprint vedi-anche"> <div class="hatnote-content"> <span class="noviewer hatnote-icon" typeof="mw:File"><span> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" decoding="async" width="18" height="18" class="mw-file-element" data-file-width="286" data-file-height="280"> </noscript><span class="lazy-image-placeholder" style="width: 18px;height: 18px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" data-width="18" data-height="18" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/27px-Magnifying_glass_icon_mgx2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/36px-Magnifying_glass_icon_mgx2.svg.png 2x" data-class="mw-file-element"> </span></span></span> <span class="hatnote-text">Lo stesso argomento in dettaglio: <b><a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Modulo_dinamico&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Modulo dinamico (la pagina non esiste)">Modulo dinamico</a></b>.</span> </div> </div> <p>La viscoelasticità viene studiata usando l'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Analisi_meccanica_dinamica?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Analisi meccanica dinamica">analisi meccanica dinamica</a> (DMA), applicando una piccola deformazione oscillatoria e misurando la tensione risultante.</p> <p>A seconda della natura del materiale, si possono avere i seguenti casi:</p> <ul> <li>i materiali puramente elastici presentano sforzo e deformazione in fase, per cui la risposta al cambiamento di uno di questi parametri influenza in maniera immediata l'altro parametro;</li> <li>nei materiali puramente viscosi, la deformazione è ritardata rispetto allo sforzo di 90°.</li> <li>i materiali viscoelastici mostrano un comportamento intermedio tra il comportamento puramente elastico e quello puramente viscoso, mostrando un valore del ritardo della deformazione rispetto allo sforzo tra 0° e 90°.</li> </ul> <p>Il <a href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Modulo_dinamico&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Modulo dinamico (la pagina non esiste)">modulo dinamico</a> complesso <i>G</i> può essere usato per rappresentare le relazioni tra lo sforzo e la deformazione in una prova dinamica:</p> <dl> <dd> <i>G = G' + iG"</i> </dd> </dl> <p>dove:</p> <ul> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i^{2}=-1}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> i </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> = </mo> <mo> −<!-- − --> </mo> <mn> 1 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i^{2}=-1} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e98a401d352e5037d5043028e2d7f449e83fa6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.926ex; height:2.843ex;" alt="{\displaystyle i^{2}=-1}"> </noscript><span class="lazy-image-placeholder" style="width: 7.926ex;height: 2.843ex;vertical-align: -0.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e98a401d352e5037d5043028e2d7f449e83fa6" data-alt="{\displaystyle i^{2}=-1}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G'}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> G </mi> <mo> ′ </mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle G'} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76634fad5818a777669a77cd8c86d1d816e4c402" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.511ex; height:2.509ex;" alt="{\displaystyle G'}"> </noscript><span class="lazy-image-placeholder" style="width: 2.511ex;height: 2.509ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76634fad5818a777669a77cd8c86d1d816e4c402" data-alt="{\displaystyle G'}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> rappresenta il contributo elastico, pari a:</li> </ul> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G'={\frac {\sigma _{0}}{\varepsilon _{0}}}\cos \delta }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> G </mi> <mo> ′ </mo> </msup> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mfrac> </mrow> <mi> cos </mi> <mo> <!-- --> </mo> <mi> δ<!-- δ --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle G'={\frac {\sigma _{0}}{\varepsilon _{0}}}\cos \delta } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/379fe483def69f428d8483045dffcb65f4be50bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.762ex; height:5.009ex;" alt="{\displaystyle G'={\frac {\sigma _{0}}{\varepsilon _{0}}}\cos \delta }"> </noscript><span class="lazy-image-placeholder" style="width: 13.762ex;height: 5.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/379fe483def69f428d8483045dffcb65f4be50bd" data-alt="{\displaystyle G'={\frac {\sigma _{0}}{\varepsilon _{0}}}\cos \delta }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <ul> <li><i>G"</i> rappresenta il contributo viscoso, pari a:</li> </ul> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G''={\frac {\sigma _{0}}{\varepsilon _{0}}}\sin \delta }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> G </mi> <mo> ″ </mo> </msup> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mfrac> </mrow> <mi> sin </mi> <mo> <!-- --> </mo> <mi> δ<!-- δ --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle G''={\frac {\sigma _{0}}{\varepsilon _{0}}}\sin \delta } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99e06a1c7b659daecf495e78bff521cc4041375e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.959ex; height:5.009ex;" alt="{\displaystyle G''={\frac {\sigma _{0}}{\varepsilon _{0}}}\sin \delta }"> </noscript><span class="lazy-image-placeholder" style="width: 13.959ex;height: 5.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99e06a1c7b659daecf495e78bff521cc4041375e" data-alt="{\displaystyle G''={\frac {\sigma _{0}}{\varepsilon _{0}}}\sin \delta }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <ul> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{0}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma _{0}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2f330c7d4a4ee92e5d43dfe3e23f0de3406ec78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.382ex; height:2.009ex;" alt="{\displaystyle \sigma _{0}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.382ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2f330c7d4a4ee92e5d43dfe3e23f0de3406ec78" data-alt="{\displaystyle \sigma _{0}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è l'ampiezza dello stress;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{0}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon _{0}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acb0a8377db20e42274444cb181d51b5532b5844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.138ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{0}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.138ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acb0a8377db20e42274444cb181d51b5532b5844" data-alt="{\displaystyle \varepsilon _{0}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è l'ampiezza della deformazione;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ<!-- δ --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 2.343ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" data-alt="{\displaystyle \delta }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è lo sfasamento tra stress e deformazione.</li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Viscoelasticità_lineare_e_non_lineare"><span id="Viscoelasticit.C3.A0_lineare_e_non_lineare"></span>Viscoelasticità lineare e non lineare</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=7&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Viscoelasticità lineare e non lineare" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-6 collapsible-block" id="mf-section-6"> <p>La <b>viscoelasticità lineare</b> si ha quando la funzione è un'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Equazione_differenziale_ordinaria?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Equazione differenziale ordinaria">equazione differenziale ordinaria</a> separabile nei confronti sia della risposta allo <a href="https://it-m-wikipedia-org.translate.goog/wiki/Scorrimento_viscoso?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Scorrimento viscoso">scorrimento viscoso</a> sia del carico applicato. Tutti i modelli viscoelastici lineari possono essere rappresentati dall'<a href="https://it-m-wikipedia-org.translate.goog/wiki/Equazione_integrale?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Equazione integrale">equazione di Volterra</a>, che lega lo sforzo e la deformazione:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon (t)={\frac {\sigma (t)}{E_{\text{inst,creep}}}}+\int _{0}^{t}K(t-t^{\prime }){\dot {\sigma }}(t^{\prime })dt^{\prime }}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> inst,creep </mtext> </mrow> </msub> </mfrac> </mrow> <mo> + </mo> <msubsup> <mo> ∫<!-- ∫ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> t </mi> </mrow> </msubsup> <mi> K </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo> −<!-- − --> </mo> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo stretchy="false"> ( </mo> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> <mo stretchy="false"> ) </mo> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon (t)={\frac {\sigma (t)}{E_{\text{inst,creep}}}}+\int _{0}^{t}K(t-t^{\prime }){\dot {\sigma }}(t^{\prime })dt^{\prime }} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd5a0d6a3c6f02d5a3680970d26da4e50cf321d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:39.48ex; height:6.343ex;" alt="{\displaystyle \varepsilon (t)={\frac {\sigma (t)}{E_{\text{inst,creep}}}}+\int _{0}^{t}K(t-t^{\prime }){\dot {\sigma }}(t^{\prime })dt^{\prime }}"> </noscript><span class="lazy-image-placeholder" style="width: 39.48ex;height: 6.343ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd5a0d6a3c6f02d5a3680970d26da4e50cf321d9" data-alt="{\displaystyle \varepsilon (t)={\frac {\sigma (t)}{E_{\text{inst,creep}}}}+\int _{0}^{t}K(t-t^{\prime }){\dot {\sigma }}(t^{\prime })dt^{\prime }}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>oppure:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma (t)=E_{\text{inst,relax}}\varepsilon (t)+\int _{0}^{t}F(t-t^{\prime }){\dot {\varepsilon }}(t^{\prime })dt^{\prime }}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> inst,relax </mtext> </mrow> </msub> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> + </mo> <msubsup> <mo> ∫<!-- ∫ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> t </mi> </mrow> </msubsup> <mi> F </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo> −<!-- − --> </mo> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo stretchy="false"> ( </mo> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> <mo stretchy="false"> ) </mo> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal"> ′<!-- ′ --> </mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma (t)=E_{\text{inst,relax}}\varepsilon (t)+\int _{0}^{t}F(t-t^{\prime }){\dot {\varepsilon }}(t^{\prime })dt^{\prime }} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40bdab38b32c5acea1aa22579a57986d5cb05a76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.097ex; height:6.176ex;" alt="{\displaystyle \sigma (t)=E_{\text{inst,relax}}\varepsilon (t)+\int _{0}^{t}F(t-t^{\prime }){\dot {\varepsilon }}(t^{\prime })dt^{\prime }}"> </noscript><span class="lazy-image-placeholder" style="width: 42.097ex;height: 6.176ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40bdab38b32c5acea1aa22579a57986d5cb05a76" data-alt="{\displaystyle \sigma (t)=E_{\text{inst,relax}}\varepsilon (t)+\int _{0}^{t}F(t-t^{\prime }){\dot {\varepsilon }}(t^{\prime })dt^{\prime }}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dove:</p> <ul> <li><i>t</i> è il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Tempo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Tempo">tempo</a>;</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma (t)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma (t)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37d0ec2fbe49749b21f2d391656ef60cfb269735" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle \sigma (t)}"> </noscript><span class="lazy-image-placeholder" style="width: 3.979ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37d0ec2fbe49749b21f2d391656ef60cfb269735" data-alt="{\displaystyle \sigma (t)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></i> è lo <a href="https://it-m-wikipedia-org.translate.goog/wiki/Azione_esterna?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Azione esterna">sforzo</a>;</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon (t)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon (t)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcc74fc545ab3f54592db8fccce157170d9a431d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.732ex; height:2.843ex;" alt="{\displaystyle \varepsilon (t)}"> </noscript><span class="lazy-image-placeholder" style="width: 3.732ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcc74fc545ab3f54592db8fccce157170d9a431d" data-alt="{\displaystyle \varepsilon (t)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></i> è la deformazione;</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{inst,creep}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> inst,creep </mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle E_{\text{inst,creep}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35972955b73b4d77e0063d102613ecc6a357caf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.812ex; height:2.843ex;" alt="{\displaystyle E_{\text{inst,creep}}}"> </noscript><span class="lazy-image-placeholder" style="width: 8.812ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35972955b73b4d77e0063d102613ecc6a357caf7" data-alt="{\displaystyle E_{\text{inst,creep}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></i> è il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Modulo_di_Young?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Modulo di Young">modulo elastico</a> istantaneo misurato nella prova di scorrimento viscoso;</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{inst,relax}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> inst,relax </mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle E_{\text{inst,relax}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0eb2a1ff6dfdbec7d3bebd84ba802e0124dfc2c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.586ex; height:2.843ex;" alt="{\displaystyle E_{\text{inst,relax}}}"> </noscript><span class="lazy-image-placeholder" style="width: 8.586ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0eb2a1ff6dfdbec7d3bebd84ba802e0124dfc2c2" data-alt="{\displaystyle E_{\text{inst,relax}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></i> è il modulo elastico istantaneo misurato nella prova di rilassamento degli sforzi;</li> <li><i>K(t)</i> è la funzione di scorrimento viscoso;</li> <li><i>F(t)</i> è la funzione di rilassamento degli sforzi.</li> </ul> <p>La viscoelasticità lineare di solito è applicabile solo nel caso di piccole <a href="https://it-m-wikipedia-org.translate.goog/wiki/Deformazione?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Deformazione">deformazioni</a>.</p> <p>La <b>viscoelasticità non lineare</b> si ha quando la funzione non è separabile; in genere ciò accade quando le <a href="https://it-m-wikipedia-org.translate.goog/wiki/Deformazione?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Deformazione">deformazioni</a> sono grandi o se il materiale cambia le sue proprietà durante la deformazione.</p> <p>Valutando il modulo elastico durante un esperimento di stress relaxation, si noterà un valore costante al variare della deformazione iniziale applicata nel caso in cui ci si trovi in regime di viscoelasticità lineare, viceversa nel caso in cui il regime fosse di viscoelasticità non lineare si otterrebbero diversi valori del modulo elastico al variare della deformazione iniziale; un analogo discorso può essere condotto nel caso in cui ad essere valutato fosse il modulo di compliance J(t) durante un esperimento di creep in regime di viscoelasticità lineare.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Equazioni_costitutive_dei_materiali_viscoelastici">Equazioni costitutive dei materiali viscoelastici</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=8&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Equazioni costitutive dei materiali viscoelastici" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-7 collapsible-block" id="mf-section-7"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139255918"> <div class="ambox avviso-mini noprint metadata avviso-mini-generico plainlinks"> <div class="mbox-text"> <div class="mbox-text-div" style="display:flex; flex-direction:row; align-items:center; column-gap:5px;"> <span style="width:100%"><b>Questa sezione sull'argomento fisica è solo un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Aiuto:Abbozzo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Aiuto:Abbozzo">abbozzo</a></b>. <a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/w/index.php?title%3DViscoelasticit%25C3%25A0%26action%3Dedit">Contribuisci</a> a migliorarla secondo le <a href="https://it-m-wikipedia-org.translate.goog/wiki/Aiuto:Manuale_di_stile?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Aiuto:Manuale di stile">convenzioni di Wikipedia</a>. Segui i suggerimenti del <a href="https://it-m-wikipedia-org.translate.goog/wiki/Progetto:Fisica?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Progetto:Fisica">progetto di riferimento</a>.</span> </div> </div> </div> <p>Detti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"> </noscript><span class="lazy-image-placeholder" style="width: 1.33ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" data-alt="{\displaystyle \sigma }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> lo sforzo, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ε<!-- ε --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"> </noscript><span class="lazy-image-placeholder" style="width: 1.083ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" data-alt="{\displaystyle \varepsilon }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è la <a href="https://it-m-wikipedia-org.translate.goog/wiki/Deformazione?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Deformazione">deformazione</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> E </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle E} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"> </noscript><span class="lazy-image-placeholder" style="width: 1.776ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" data-alt="{\displaystyle E}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Modulo_di_elasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modulo di elasticità">modulo elasticità di Young</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> C </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle C} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"> </noscript><span class="lazy-image-placeholder" style="width: 1.766ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" data-alt="{\displaystyle C}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> il modulo di cedevolezza e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> t </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle t} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"> </noscript><span class="lazy-image-placeholder" style="width: 0.84ex;height: 2.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" data-alt="{\displaystyle t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> il <a href="https://it-m-wikipedia-org.translate.goog/wiki/Tempo?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Tempo">tempo</a>.</p> <div class="mw-heading mw-heading3"> <h3 id="Modelli_a_2_elementi">Modelli a 2 elementi</h3><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=9&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modelli a 2 elementi" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <div class="mw-heading mw-heading4"> <h4 id="Modello_di_Maxwell">Modello di Maxwell</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=10&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello di Maxwell" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <p>Il <b>modello di Maxwell</b> descrive bene i materiali viscoelastici che si comportano in modo elastico su intervalli di tempo brevi e in modo viscoso su intervalli di tempo lunghi. In genere il modello di Maxwell viene impiegato per prevedere il comportamento dei materiali viscoelastici liquidi.</p> <figure class="mw-default-size" typeof="mw:File/Thumb"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:Maxwell_diagram.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Maxwell_diagram.svg/220px-Maxwell_diagram.svg.png" decoding="async" width="220" height="60" class="mw-file-element" data-file-width="330" data-file-height="90"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 60px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Maxwell_diagram.svg/220px-Maxwell_diagram.svg.png" data-width="220" data-height="60" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Maxwell_diagram.svg/330px-Maxwell_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Maxwell_diagram.svg/440px-Maxwell_diagram.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Analogia meccanica del modello di Maxwell </figcaption> </figure> <p>Tale modello è rappresentato da un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Dissipatore_viscoso?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Dissipatore viscoso">dissipatore viscoso</a> collegato in serie a una <a href="https://it-m-wikipedia-org.translate.goog/wiki/Molla?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Molla">molla</a>. Ad esso associata è la seguente equazione, che descrive il sistema sommando i due contributi:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\varepsilon }}_{tot}={\dot {\varepsilon }}_{1}+{\dot {\varepsilon }}_{2}={\frac {\sigma }{\eta }}+{\frac {\dot {\sigma }}{E}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> t </mi> <mi> o </mi> <mi> t </mi> </mrow> </msub> <mo> = </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> σ<!-- σ --> </mi> <mi> η<!-- η --> </mi> </mfrac> </mrow> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> <mi> E </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\dot {\varepsilon }}_{tot}={\dot {\varepsilon }}_{1}+{\dot {\varepsilon }}_{2}={\frac {\sigma }{\eta }}+{\frac {\dot {\sigma }}{E}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b471f46cbdf4f3a178a3eacc19b18c292c045d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.049ex; height:5.676ex;" alt="{\displaystyle {\dot {\varepsilon }}_{tot}={\dot {\varepsilon }}_{1}+{\dot {\varepsilon }}_{2}={\frac {\sigma }{\eta }}+{\frac {\dot {\sigma }}{E}}}"> </noscript><span class="lazy-image-placeholder" style="width: 25.049ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b471f46cbdf4f3a178a3eacc19b18c292c045d" data-alt="{\displaystyle {\dot {\varepsilon }}_{tot}={\dot {\varepsilon }}_{1}+{\dot {\varepsilon }}_{2}={\frac {\sigma }{\eta }}+{\frac {\dot {\sigma }}{E}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>in cui:</p> <ul> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{1}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon _{1}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e900f9bee793f99d10877ef108da074cbca60ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.138ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{1}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.138ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e900f9bee793f99d10877ef108da074cbca60ce" data-alt="{\displaystyle \varepsilon _{1}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è la deformazione legata al contributo viscoso</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon _{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/453175f483471f03e90376edf8b31faeccd83e28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.138ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.138ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/453175f483471f03e90376edf8b31faeccd83e28" data-alt="{\displaystyle \varepsilon _{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è la deformazione legata al contributo elastico</li> </ul> <p>Imponendo come condizioni al contorno:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=\varepsilon _{0}\\\sigma (t_{0})=\sigma _{0}=E\cdot \varepsilon _{0}\end{cases}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo> { </mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mtd> </mtr> <mtr> <mtd> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> = </mo> <mi> E </mi> <mo> ⋅<!-- ⋅ --> </mo> <msub> <mi> ε<!-- ε --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=\varepsilon _{0}\\\sigma (t_{0})=\sigma _{0}=E\cdot \varepsilon _{0}\end{cases}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0494bd3c6fd2535e7d678727b01cf462de235c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:22.021ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=\varepsilon _{0}\\\sigma (t_{0})=\sigma _{0}=E\cdot \varepsilon _{0}\end{cases}}}"> </noscript><span class="lazy-image-placeholder" style="width: 22.021ex;height: 8.509ex;vertical-align: -3.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0494bd3c6fd2535e7d678727b01cf462de235c3" data-alt="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=\varepsilon _{0}\\\sigma (t_{0})=\sigma _{0}=E\cdot \varepsilon _{0}\end{cases}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>si ottiene</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma (t)=\sigma _{0}\exp \left(-{\frac {t}{t_{ril}}}\right)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mi> exp </mi> <mo> <!-- --> </mo> <mrow> <mo> ( </mo> <mrow> <mo> −<!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> t </mi> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> r </mi> <mi> i </mi> <mi> l </mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma (t)=\sigma _{0}\exp \left(-{\frac {t}{t_{ril}}}\right)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e907c0b46a05604633d0a87eddf863dcb81eb3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.335ex; height:6.176ex;" alt="{\displaystyle \sigma (t)=\sigma _{0}\exp \left(-{\frac {t}{t_{ril}}}\right)}"> </noscript><span class="lazy-image-placeholder" style="width: 22.335ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e907c0b46a05604633d0a87eddf863dcb81eb3d" data-alt="{\displaystyle \sigma (t)=\sigma _{0}\exp \left(-{\frac {t}{t_{ril}}}\right)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{ril}={\frac {\eta }{E}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> r </mi> <mi> i </mi> <mi> l </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> η<!-- η --> </mi> <mi> E </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle t_{ril}={\frac {\eta }{E}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1a7069685a92fb1a7c3ae3aa3fe2c30dc312688" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.581ex; height:4.843ex;" alt="{\displaystyle t_{ril}={\frac {\eta }{E}}}"> </noscript><span class="lazy-image-placeholder" style="width: 8.581ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1a7069685a92fb1a7c3ae3aa3fe2c30dc312688" data-alt="{\displaystyle t_{ril}={\frac {\eta }{E}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading4"> <h4 id="Modello_di_Kelvin-Voigt">Modello di Kelvin-Voigt</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=11&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello di Kelvin-Voigt" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <p>In genere il <b>modello di Kelvin-Voigt</b> viene impiegato per prevedere il comportamento dei materiali viscoelastici solidi.</p> <figure typeof="mw:File/Thumb"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:Kelvin_Voigt_diagram.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Kelvin_Voigt_diagram.svg/150px-Kelvin_Voigt_diagram.svg.png" decoding="async" width="150" height="113" class="mw-file-element" data-file-width="200" data-file-height="150"> </noscript><span class="lazy-image-placeholder" style="width: 150px;height: 113px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Kelvin_Voigt_diagram.svg/150px-Kelvin_Voigt_diagram.svg.png" data-alt="" data-width="150" data-height="113" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Kelvin_Voigt_diagram.svg/225px-Kelvin_Voigt_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Kelvin_Voigt_diagram.svg/300px-Kelvin_Voigt_diagram.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Analogia meccanica del modello di Kelvin-Voigt. </figcaption> </figure> <p>Tale modello è rappresentato da un dissipatore viscoso collegato in parallelo a una molla e l'equazione costitutiva ad esso associata è la seguente:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{tot}=\sigma _{1}+\sigma _{2}=E\cdot \varepsilon +\eta \cdot {\dot {\varepsilon }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> t </mi> <mi> o </mi> <mi> t </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo> = </mo> <mi> E </mi> <mo> ⋅<!-- ⋅ --> </mo> <mi> ε<!-- ε --> </mi> <mo> + </mo> <mi> η<!-- η --> </mi> <mo> ⋅<!-- ⋅ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma _{tot}=\sigma _{1}+\sigma _{2}=E\cdot \varepsilon +\eta \cdot {\dot {\varepsilon }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4508d3008f83a4649bd216bb9335c38d5c0a5a8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.928ex; height:2.676ex;" alt="{\displaystyle \sigma _{tot}=\sigma _{1}+\sigma _{2}=E\cdot \varepsilon +\eta \cdot {\dot {\varepsilon }}}"> </noscript><span class="lazy-image-placeholder" style="width: 28.928ex;height: 2.676ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4508d3008f83a4649bd216bb9335c38d5c0a5a8a" data-alt="{\displaystyle \sigma _{tot}=\sigma _{1}+\sigma _{2}=E\cdot \varepsilon +\eta \cdot {\dot {\varepsilon }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>in cui:</p> <ul> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{1}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma _{1}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa0e56273a1cb32709b442e2421e9f947522b84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.382ex; height:2.009ex;" alt="{\displaystyle \sigma _{1}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.382ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa0e56273a1cb32709b442e2421e9f947522b84" data-alt="{\displaystyle \sigma _{1}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è lo sforzo legato al contributo elastico</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma _{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4b9cd9efc54bcfd04e0a2231913c13f10798d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.382ex; height:2.009ex;" alt="{\displaystyle \sigma _{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.382ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4b9cd9efc54bcfd04e0a2231913c13f10798d9" data-alt="{\displaystyle \sigma _{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> è lo sforzo legato al contributo viscoso</li> </ul> <p>Imponendo come condizioni al contorno:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=0\\\sigma (t_{0})=\sigma _{0}\end{cases}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo> { </mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mtd> </mtr> <mtr> <mtd> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> = </mo> <mn> 0 </mn> </mtd> </mtr> <mtr> <mtd> <mi> σ<!-- σ --> </mi> <mo stretchy="false"> ( </mo> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=0\\\sigma (t_{0})=\sigma _{0}\end{cases}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5521c825c43ac1fd5e5e51329fda4e281580cc28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:13.33ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=0\\\sigma (t_{0})=\sigma _{0}\end{cases}}}"> </noscript><span class="lazy-image-placeholder" style="width: 13.33ex;height: 8.509ex;vertical-align: -3.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5521c825c43ac1fd5e5e51329fda4e281580cc28" data-alt="{\displaystyle {\begin{cases}t_{0}=0\\\varepsilon (t_{0})=0\\\sigma (t_{0})=\sigma _{0}\end{cases}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>si ottiene</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon (t)=C\sigma _{0}\left[1-\exp \left(-{\frac {t}{t_{rit}}}\right)\right]}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ε<!-- ε --> </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mi> C </mi> <msub> <mi> σ<!-- σ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mrow> <mo> [ </mo> <mrow> <mn> 1 </mn> <mo> −<!-- − --> </mo> <mi> exp </mi> <mo> <!-- --> </mo> <mrow> <mo> ( </mo> <mrow> <mo> −<!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> t </mi> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> r </mi> <mi> i </mi> <mi> t </mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ] </mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varepsilon (t)=C\sigma _{0}\left[1-\exp \left(-{\frac {t}{t_{rit}}}\right)\right]} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b762e971f80ef6bd9f724352e273b2059c7a00b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.416ex; height:6.176ex;" alt="{\displaystyle \varepsilon (t)=C\sigma _{0}\left[1-\exp \left(-{\frac {t}{t_{rit}}}\right)\right]}"> </noscript><span class="lazy-image-placeholder" style="width: 30.416ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b762e971f80ef6bd9f724352e273b2059c7a00b8" data-alt="{\displaystyle \varepsilon (t)=C\sigma _{0}\left[1-\exp \left(-{\frac {t}{t_{rit}}}\right)\right]}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{rit}={\frac {\eta }{E}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> r </mi> <mi> i </mi> <mi> t </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> η<!-- η --> </mi> <mi> E </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle t_{rit}={\frac {\eta }{E}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1d0df9e51d9e8973696ae30aaec004f47fc286e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.685ex; height:4.843ex;" alt="{\displaystyle t_{rit}={\frac {\eta }{E}}}"> </noscript><span class="lazy-image-placeholder" style="width: 8.685ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1d0df9e51d9e8973696ae30aaec004f47fc286e" data-alt="{\displaystyle t_{rit}={\frac {\eta }{E}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Modelli_a_3_elementi">Modelli a 3 elementi</h3><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=12&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modelli a 3 elementi" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <div class="mw-heading mw-heading4"> <h4 id="Modello_lineare_standard_di_Zener">Modello lineare standard di Zener</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=13&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello lineare standard di Zener" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <p>Il <b>modello lineare standard</b>, proposto per la prima volta da <a href="https://it-m-wikipedia-org.translate.goog/wiki/Clarence_Zener?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Clarence Zener">Clarence Zener</a>, è un modello ideato per risolvere le problematiche dei modelli a due elementi. Può essere rappresentato da una molla collegata in parallelo ad un dissipatore viscoso e una molla collegati a loro volta in serie, secondo la rappresentazione di Maxwell, o da una molla in serie a un pistone e una molla posti in parallelo, secondo la rappresentazione di Kelvin-Voigt.</p> <table class="wikitable"> <tbody> <tr> <th>Rappresentazione di Maxwell</th> <th>Rappresentazione di Kelvin-Voigt</th> </tr> <tr> <td> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Frameless"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:SLS.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/SLS.svg/220px-SLS.svg.png" decoding="async" width="220" height="160" class="mw-file-element" data-file-width="330" data-file-height="240"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 160px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/SLS.svg/220px-SLS.svg.png" data-alt="" data-width="220" data-height="160" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/SLS.svg/330px-SLS.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/SLS.svg/440px-SLS.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption></figcaption> </figure></td> <td> <figure class="mw-halign-center" typeof="mw:File/Frameless"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:SLS2.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/SLS2.svg/200px-SLS2.svg.png" decoding="async" width="200" height="160" class="mw-file-element" data-file-width="300" data-file-height="240"> </noscript><span class="lazy-image-placeholder" style="width: 200px;height: 160px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/SLS2.svg/200px-SLS2.svg.png" data-alt="" data-width="200" data-height="160" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/SLS2.svg/300px-SLS2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/SLS2.svg/400px-SLS2.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption></figcaption> </figure></td> </tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma +{\frac {\eta }{E_{2}}}{\dot {\sigma }}=E_{1}\varepsilon +{\frac {\eta (E_{1}+E_{2})}{E_{2}}}{\dot {\varepsilon }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> η<!-- η --> </mi> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> = </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mi> ε<!-- ε --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> η<!-- η --> </mi> <mo stretchy="false"> ( </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> </mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma +{\frac {\eta }{E_{2}}}{\dot {\sigma }}=E_{1}\varepsilon +{\frac {\eta (E_{1}+E_{2})}{E_{2}}}{\dot {\varepsilon }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7151a4899b7afd5aa5e3183e55357314ae3d4ea0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:32.447ex; height:6.009ex;" alt="{\displaystyle \sigma +{\frac {\eta }{E_{2}}}{\dot {\sigma }}=E_{1}\varepsilon +{\frac {\eta (E_{1}+E_{2})}{E_{2}}}{\dot {\varepsilon }}}"> </noscript><span class="lazy-image-placeholder" style="width: 32.447ex;height: 6.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7151a4899b7afd5aa5e3183e55357314ae3d4ea0" data-alt="{\displaystyle \sigma +{\frac {\eta }{E_{2}}}{\dot {\sigma }}=E_{1}\varepsilon +{\frac {\eta (E_{1}+E_{2})}{E_{2}}}{\dot {\varepsilon }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma +{\frac {\eta }{E_{1}+E_{2}}}{\dot {\sigma }}={\frac {E_{1}E_{2}}{E_{1}+E_{2}}}\varepsilon +{\frac {E_{1}\eta }{E_{1}+E_{2}}}{\dot {\varepsilon }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> η<!-- η --> </mi> <mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> <mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mi> ε<!-- ε --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mi> η<!-- η --> </mi> </mrow> <mrow> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> E </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma +{\frac {\eta }{E_{1}+E_{2}}}{\dot {\sigma }}={\frac {E_{1}E_{2}}{E_{1}+E_{2}}}\varepsilon +{\frac {E_{1}\eta }{E_{1}+E_{2}}}{\dot {\varepsilon }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec4c980128a036e9a6dc8e3feec7818b4b6e47bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:41.524ex; height:5.676ex;" alt="{\displaystyle \sigma +{\frac {\eta }{E_{1}+E_{2}}}{\dot {\sigma }}={\frac {E_{1}E_{2}}{E_{1}+E_{2}}}\varepsilon +{\frac {E_{1}\eta }{E_{1}+E_{2}}}{\dot {\varepsilon }}}"> </noscript><span class="lazy-image-placeholder" style="width: 41.524ex;height: 5.676ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec4c980128a036e9a6dc8e3feec7818b4b6e47bd" data-alt="{\displaystyle \sigma +{\frac {\eta }{E_{1}+E_{2}}}{\dot {\sigma }}={\frac {E_{1}E_{2}}{E_{1}+E_{2}}}\varepsilon +{\frac {E_{1}\eta }{E_{1}+E_{2}}}{\dot {\varepsilon }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> </tbody> </table> <div class="mw-heading mw-heading4"> <h4 id="Modello_di_Jeffreys-Lethersich">Modello di Jeffreys-Lethersich</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=14&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello di Jeffreys-Lethersich" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <table class="wikitable"> <tbody> <tr> <th>Rappresentazione di Jeffreys</th> <th>Rappresentazione di Lethersich</th> </tr> <tr> <td> <figure class="mw-halign-center" typeof="mw:File/Frameless"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:Jeffreys_rheological_model.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Jeffreys_rheological_model.svg/120px-Jeffreys_rheological_model.svg.png" decoding="async" width="120" height="205" class="mw-file-element" data-file-width="269" data-file-height="459"> </noscript><span class="lazy-image-placeholder" style="width: 120px;height: 205px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Jeffreys_rheological_model.svg/120px-Jeffreys_rheological_model.svg.png" data-width="120" data-height="205" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Jeffreys_rheological_model.svg/180px-Jeffreys_rheological_model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Jeffreys_rheological_model.svg/240px-Jeffreys_rheological_model.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption></figcaption> </figure></td> <td> <figure class="mw-halign-center" typeof="mw:File/Frameless"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:Letherisch-rheological-model.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Letherisch-rheological-model.svg/120px-Letherisch-rheological-model.svg.png" decoding="async" width="120" height="270" class="mw-file-element" data-file-width="252" data-file-height="568"> </noscript><span class="lazy-image-placeholder" style="width: 120px;height: 270px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Letherisch-rheological-model.svg/120px-Letherisch-rheological-model.svg.png" data-width="120" data-height="270" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Letherisch-rheological-model.svg/179px-Letherisch-rheological-model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Letherisch-rheological-model.svg/239px-Letherisch-rheological-model.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption></figcaption> </figure></td> </tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma +{\frac {\eta _{1}+\eta _{2}}{E}}{\dot {\sigma }}=\eta _{2}\cdot {\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> <mi> E </mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> = </mo> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo> ⋅<!-- ⋅ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> <mi> E </mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ¨<!-- ¨ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma +{\frac {\eta _{1}+\eta _{2}}{E}}{\dot {\sigma }}=\eta _{2}\cdot {\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12527118e760af6ea6bcb32f7458faebe58afef8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.391ex; height:5.176ex;" alt="{\displaystyle \sigma +{\frac {\eta _{1}+\eta _{2}}{E}}{\dot {\sigma }}=\eta _{2}\cdot {\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}"> </noscript><span class="lazy-image-placeholder" style="width: 31.391ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12527118e760af6ea6bcb32f7458faebe58afef8" data-alt="{\displaystyle \sigma +{\frac {\eta _{1}+\eta _{2}}{E}}{\dot {\sigma }}=\eta _{2}\cdot {\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma +{\frac {\eta _{1}}{E}}{\dot {\sigma }}=(\eta _{1}+\eta _{2}){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> σ<!-- σ --> </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mi> E </mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> σ<!-- σ --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> = </mo> <mo stretchy="false"> ( </mo> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <msub> <mi> η<!-- η --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> <mi> E </mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ε<!-- ε --> </mi> <mo> ¨<!-- ¨ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sigma +{\frac {\eta _{1}}{E}}{\dot {\sigma }}=(\eta _{1}+\eta _{2}){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632c4d182650384cdb8957ffbdc574c8e6ad5478" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.521ex; height:4.843ex;" alt="{\displaystyle \sigma +{\frac {\eta _{1}}{E}}{\dot {\sigma }}=(\eta _{1}+\eta _{2}){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}"> </noscript><span class="lazy-image-placeholder" style="width: 31.521ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632c4d182650384cdb8957ffbdc574c8e6ad5478" data-alt="{\displaystyle \sigma +{\frac {\eta _{1}}{E}}{\dot {\sigma }}=(\eta _{1}+\eta _{2}){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E}}{\ddot {\varepsilon }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> </tbody> </table> <div class="mw-heading mw-heading3"> <h3 id="Modello_a_4_elementi_di_Alfrey-Burgers">Modello a 4 elementi di Alfrey-Burgers</h3><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=15&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello a 4 elementi di Alfrey-Burgers" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139255918"> <div class="ambox avviso-mini noprint metadata avviso-mini-informazioni plainlinks"> <div class="mbox-text"> <div class="mbox-text-div" style="display:flex; flex-direction:row; align-items:center; column-gap:5px;"> <span style="width:100%"><b>Questa sezione sull'argomento fisica è ancora vuota</b>. <a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/w/index.php?title%3DViscoelasticit%25C3%25A0%26action%3Dedit">Aiutaci</a> a scriverla!</span> </div> </div> </div> <div class="mw-heading mw-heading3"> <h3 id="Modelli_Multi-elemento">Modelli Multi-elemento</h3><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=16&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modelli Multi-elemento" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <div class="mw-heading mw-heading4"> <h4 id="Modello_di_Maxwell-Weichert">Modello di Maxwell-Weichert</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=17&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello di Maxwell-Weichert" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"> <a href="https://it-m-wikipedia-org.translate.goog/wiki/File:Weichert.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Weichert.svg/220px-Weichert.svg.png" decoding="async" width="220" height="165" class="mw-file-element" data-file-width="400" data-file-height="300"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 165px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Weichert.svg/220px-Weichert.svg.png" data-width="220" data-height="165" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Weichert.svg/330px-Weichert.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Weichert.svg/440px-Weichert.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Analogia meccanica del modello di Maxwell-Weichert. </figcaption> </figure> <p>Il <b>modello di Maxwell-Weichert</b> è rappresentato da una molla collegata in parallelo a più dissipatori viscosi e molle collegate a loro volta in serie. Il <b>modello di Maxwell generalizzato</b> è rappresentato da più elementi disposti in parallelo, ciascuno a sua volta costituito da una molla e da un dissipatore viscoso disposti in serie.</p> <div class="mw-heading mw-heading4"> <h4 id="Modello_di_Kelvin-Voigt-Weichert">Modello di Kelvin-Voigt-Weichert</h4><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=18&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Modello di Kelvin-Voigt-Weichert" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <p>Il <b>modello di Kelvin-Voigt generalizzato</b> è rappresentato da più elementi disposti in serie, ciascuno a sua volta costituito da una molla e da un dissipatore viscoso disposti in parallelo.</p> <p>Il modello di Kelvin-Voigt generalizzato coincide con il modello di Maxwell generalizzato nel caso in cui il numero di elementi tende ad infinito.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Rilassamento_viscoelastico">Rilassamento viscoelastico</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=19&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Rilassamento viscoelastico" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-8 collapsible-block" id="mf-section-8"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r130657691"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r139142988"> <div class="hatnote noprint vedi-anche"> <div class="hatnote-content"> <span class="noviewer hatnote-icon" typeof="mw:File"><span> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" decoding="async" width="18" height="18" class="mw-file-element" data-file-width="286" data-file-height="280"> </noscript><span class="lazy-image-placeholder" style="width: 18px;height: 18px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/18px-Magnifying_glass_icon_mgx2.svg.png" data-width="18" data-height="18" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/27px-Magnifying_glass_icon_mgx2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Magnifying_glass_icon_mgx2.svg/36px-Magnifying_glass_icon_mgx2.svg.png 2x" data-class="mw-file-element"> </span></span></span> <span class="hatnote-text">Lo stesso argomento in dettaglio: <b><a href="https://it-m-wikipedia-org.translate.goog/wiki/Rilassamento_degli_sforzi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rilassamento degli sforzi">Rilassamento degli sforzi</a></b>.</span> </div> </div> <p>In materiali come i <a href="https://it-m-wikipedia-org.translate.goog/wiki/Polimeri_termoplastici?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Polimeri termoplastici">polimeri termoplastici</a> si osserva un <a href="https://it-m-wikipedia-org.translate.goog/wiki/Rilassamento_degli_sforzi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rilassamento degli sforzi">rilassamento delle tensioni</a>, detto anche <b>rilassamento viscoelastico</b>, portate a seguito di una certa deformazione imposta, il fenomeno si spiega con lo sgrovigliamento delle catene macromolecolari, sgrovigliamento che necessita di un certo tempo per compiersi.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Note">Note</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=20&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Note" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-9 collapsible-block" id="mf-section-9"> <div class="mw-references-wrap"> <ol class="references"> <li id="cite_note-McCrum-1"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-McCrum_1-0">a</a></i></sup> <sup><i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-McCrum_1-1">b</a></i></sup></span> <span class="reference-text">McCrum, Buckley, and Bucknell (2003): "Principles of Polymer Engineering," 117-176.</span></li> <li id="cite_note-Meyers-2"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Meyers_2-0">a</a></i></sup> <sup><i><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscoelasticit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Meyers_2-1">b</a></i></sup></span> <span class="reference-text">Meyers and Chawla (1999): "Mechanical Behavior of Materials," 98-103.</span></li> </ol> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(10)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=21&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Bibliografia" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-10 collapsible-block" id="mf-section-10"> <ul> <li>Silbey and Alberty (2001): <i>Physical Chemistry</i>, 857. John Wiley & Sons, Inc.</li> <li>Allen and Thomas (1999): "The Structure of Materials," 51.</li> <li>Crandal et al. (1999): "An Introduction to the Mechanics of Solids" 348</li> <li>J. Lemaitre and J.L. Chaboche (1994)" Mechanics of solid materials"</li> <li><cite id="CITEREFCallister" class="citation libro" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) William D. Callister, <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://books.google.it/books?id%3DhFoEAAAACAAJ%26source%3Dgbs_navlinks_s"><span style="font-style:italic;">Material Science and Engineering: An Introduction</span></a>, 5ª ed., John Wiley & Sons Inc, 1999, pp. 464-467, <a href="https://it-m-wikipedia-org.translate.goog/wiki/ISBN?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="ISBN">ISBN</a> <a href="https://it-m-wikipedia-org.translate.goog/wiki/Speciale:RicercaISBN/0-471-35243-8?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Speciale:RicercaISBN/0-471-35243-8">0-471-35243-8</a>.</cite></li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(11)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=22&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Voci correlate" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-11 collapsible-block" id="mf-section-11"> <ul> <li><a href="https://it-m-wikipedia-org.translate.goog/wiki/Polimero?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Polimero">Polimero</a></li> <li><a href="https://it-m-wikipedia-org.translate.goog/wiki/Viscosit%C3%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Viscosità">Viscosità</a></li> <li><a href="https://it-m-wikipedia-org.translate.goog/wiki/Reologia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Reologia">Reologia</a></li> <li><a href="https://it-m-wikipedia-org.translate.goog/wiki/Fluido_alla_Boger?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Fluido alla Boger">Fluido alla Boger</a></li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(12)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=23&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Altri progetti" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-12 collapsible-block" id="mf-section-12"> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"> <p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p> <ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wiktionary.org/wiki/viscoelasticit%25C3%25A0" class="extiw" title="wikt:viscoelasticità">Wikizionario</a></li> <li class="" title=""><span class="plainlinks" title="commons:Category:Viscoelasticity"><a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://commons.wikimedia.org/wiki/Category:Viscoelasticity?uselang%3Dit">Wikimedia Commons</a></span></li> </ul> </div> <ul> <li><span typeof="mw:File"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"> <noscript> <img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" data-file-width="350" data-file-height="350"> </noscript><span class="lazy-image-placeholder" style="width: 18px;height: 18px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" data-alt="Collabora a Wikizionario" data-width="18" data-height="18" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/27px-Wiktionary_small.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/36px-Wiktionary_small.svg.png 2x" data-class="mw-file-element"> </span></a></span> <a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wiktionary.org/wiki/viscoelasticit%25C3%25A0" class="extiw" title="wikt:viscoelasticità">viscoelasticità</a></b>»</li> <li><span typeof="mw:File"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://commons.wikimedia.org/wiki/?uselang%3Dit" title="Collabora a Wikimedia Commons"> <noscript> <img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" data-file-width="1024" data-file-height="1376"> </noscript><span class="lazy-image-placeholder" style="width: 18px;height: 24px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" data-alt="Collabora a Wikimedia Commons" data-width="18" data-height="24" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-class="mw-file-element"> </span></a></span> <span class="plainlinks"><a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://commons.wikimedia.org/wiki/?uselang%3Dit">Wikimedia Commons</a></span> contiene immagini o altri file sulla <b><span class="plainlinks"><a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://commons.wikimedia.org/wiki/Category:Viscoelasticity?uselang%3Dit">viscoelasticità</a></span></b></li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(13)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"> <a role="button" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=edit&section=24&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Modifica la sezione Collegamenti esterni" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>modifica</span> </a> </span> </div> <section class="mf-section-13 collapsible-block" id="mf-section-13"> <ul> <li class="mw-empty-elt"></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.britannica.com/science/viscoelasticity"><span style="font-style:italic;">viscoelasticity</span></a>, su <span style="font-style:italic;"><a href="https://it-m-wikipedia-org.translate.goog/wiki/Enciclopedia_Britannica?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.wikidata.org/wiki/Q910483%23P1417" title="Modifica su Wikidata"> <noscript> <img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" data-file-width="600" data-file-height="600"> </noscript><span class="lazy-image-placeholder" style="width: 10px;height: 10px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" data-alt="Modifica su Wikidata" data-width="10" data-height="10" 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Rendering was triggered because: page-view --> </section> </div><!-- MobileFormatter took 0.018 seconds --><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --> <noscript> <img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=mobile" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Estratto da "<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/w/index.php?title%3DViscoelasticit%C3%A0%26oldid%3D140720877">https://it.wikipedia.org/w/index.php?title=Viscoelasticità&oldid=140720877</a>" </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://it-m-wikipedia-org.translate.goog/w/index.php?title=Viscoelasticit%C3%A0&action=history&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"> <div class="post-content last-modified-bar__content"><span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="151.43.29.123" data-user-gender="unknown" data-timestamp="1724141698"> <span>Ultima modifica il 20 ago 2024 alle 09:14</span> </span> <span class="minerva-icon minerva-icon-size-small minerva-icon--expand"></span> </div></a> <div class="post-content footer-content"> <div id="mw-data-after-content"> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Lingue</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ar.wikipedia.org/wiki/%25D9%2585%25D8%25B1%25D9%2588%25D9%2586%25D8%25A9_%25D9%2584%25D8%25B2%25D9%2588%25D8%25AC%25D9%258A%25D8%25A9" title="مرونة لزوجية - arabo" lang="ar" hreflang="ar" data-title="مرونة لزوجية" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ca.wikipedia.org/wiki/Viscoelasticitat" title="Viscoelasticitat - catalano" lang="ca" hreflang="ca" data-title="Viscoelasticitat" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wikipedia.org/wiki/Viskoelastizit%25C3%25A4t" title="Viskoelastizität - tedesco" lang="de" hreflang="de" data-title="Viskoelastizität" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikipedia.org/wiki/Viscoelasticity" title="Viscoelasticity - inglese" lang="en" hreflang="en" data-title="Viscoelasticity" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li> <li class="interlanguage-link interwiki-es mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://es.wikipedia.org/wiki/Viscoelasticidad" title="Viscoelasticidad - spagnolo" lang="es" hreflang="es" data-title="Viscoelasticidad" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li> <li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fa.wikipedia.org/wiki/%25D9%2588%25DB%258C%25D8%25B3%25DA%25A9%25D9%2588%25D8%25A7%25D9%2584%25D8%25A7%25D8%25B3%25D8%25AA%25DB%258C%25D8%25B3%25DB%258C%25D8%25AA%25D9%2587_(%25D9%2585%25DA%25A9%25D8%25A7%25D9%2586%25DB%258C%25DA%25A9)" title="ویسکوالاستیسیته (مکانیک) - persiano" lang="fa" hreflang="fa" data-title="ویسکوالاستیسیته (مکانیک)" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li> <li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fi.wikipedia.org/wiki/Viskoelastisuus" title="Viskoelastisuus - finlandese" lang="fi" hreflang="fi" data-title="Viskoelastisuus" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li> <li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fr.wikipedia.org/wiki/Visco%25C3%25A9lasticit%25C3%25A9" title="Viscoélasticité - francese" lang="fr" hreflang="fr" data-title="Viscoélasticité" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li> <li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ga.wikipedia.org/wiki/Slaodleaisteachas" title="Slaodleaisteachas - irlandese" lang="ga" hreflang="ga" data-title="Slaodleaisteachas" data-language-autonym="Gaeilge" data-language-local-name="irlandese" class="interlanguage-link-target"><span>Gaeilge</span></a></li> <li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://gl.wikipedia.org/wiki/Viscoelasticidade" title="Viscoelasticidade - galiziano" lang="gl" hreflang="gl" data-title="Viscoelasticidade" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ja.wikipedia.org/wiki/%25E7%25B2%2598%25E5%25BC%25BE%25E6%2580%25A7" title="粘弾性 - giapponese" lang="ja" hreflang="ja" data-title="粘弾性" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li> <li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ko.wikipedia.org/wiki/%25EC%25A0%2590%25ED%2583%2584%25EC%2584%25B1" title="점탄성 - coreano" lang="ko" hreflang="ko" data-title="점탄성" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li> <li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ky.wikipedia.org/wiki/%25D0%2598%25D0%25BB%25D1%258D%25D1%258D%25D1%2588%25D0%25BA%25D0%25B5%25D0%25BA%25D1%2582%25D2%25AF%25D2%25AF_%25D1%2581%25D0%25B5%25D1%2580%25D0%25BF%25D0%25B8%25D0%25BB%25D0%25B3%25D0%25B8%25D1%2587%25D1%2582%25D0%25B8%25D0%25BA" title="Илээшкектүү серпилгичтик - kirghiso" lang="ky" hreflang="ky" data-title="Илээшкектүү серпилгичтик" data-language-autonym="Кыргызча" data-language-local-name="kirghiso" class="interlanguage-link-target"><span>Кыргызча</span></a></li> <li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://lv.wikipedia.org/wiki/Viskoelast%25C4%25ABba" title="Viskoelastība - lettone" lang="lv" hreflang="lv" data-title="Viskoelastība" data-language-autonym="Latviešu" data-language-local-name="lettone" class="interlanguage-link-target"><span>Latviešu</span></a></li> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nn.wikipedia.org/wiki/Viskoelastisitet" title="Viskoelastisitet - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Viskoelastisitet" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://no.wikipedia.org/wiki/Viskoelastisitet" title="Viskoelastisitet - norvegese bokmål" lang="nb" hreflang="nb" data-title="Viskoelastisitet" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pt.wikipedia.org/wiki/Viscoelasticidade" title="Viscoelasticidade - portoghese" lang="pt" hreflang="pt" data-title="Viscoelasticidade" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li> <li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ru.wikipedia.org/wiki/%25D0%2592%25D1%258F%25D0%25B7%25D0%25BA%25D0%25BE%25D1%2583%25D0%25BF%25D1%2580%25D1%2583%25D0%25B3%25D0%25BE%25D1%2581%25D1%2582%25D1%258C" title="Вязкоупругость - russo" lang="ru" hreflang="ru" data-title="Вязкоупругость" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li> <li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sv.wikipedia.org/wiki/Viskoelasticitet" title="Viskoelasticitet - svedese" lang="sv" hreflang="sv" data-title="Viskoelasticitet" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li> <li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uk.wikipedia.org/wiki/%25D0%2592%2527%25D1%258F%25D0%25B7%25D0%25BA%25D0%25BE%25D0%25B5%25D0%25BB%25D0%25B0%25D1%2581%25D1%2582%25D0%25B8%25D1%2587%25D0%25BD%25D1%2596%25D1%2581%25D1%2582%25D1%258C" title="В'язкоеластичність - ucraino" lang="uk" hreflang="uk" data-title="В'язкоеластичність" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li> <li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://vi.wikipedia.org/wiki/Nh%25E1%25BB%259Bt_%25C4%2591%25C3%25A0n_h%25E1%25BB%2593i" title="Nhớt đàn hồi - vietnamita" lang="vi" hreflang="vi" data-title="Nhớt đàn hồi" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> <li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh.wikipedia.org/wiki/%25E9%25BB%258F%25E5%25BC%25B9%25E6%2580%25A7" title="黏弹性 - cinese" lang="zh" hreflang="zh" data-title="黏弹性" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li> <li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh-min-nan.wikipedia.org/wiki/Li%25C3%25A2m-t%25C3%25A2n-s%25C3%25A8ng" 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