Deformasjon – Wikipedia

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href="/w/index.php?title=Spesial:Logg_inn&returnto=Deformasjon" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Nettsted"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Innhold" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Til toppen)</div> </a> </li> <li id="toc-Typer_deformasjon" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typer_deformasjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Typer deformasjon</span> </div> </a> <button aria-controls="toc-Typer_deformasjon-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Typer deformasjon</span> </button> <ul id="toc-Typer_deformasjon-sublist" class="vector-toc-list"> <li id="toc-Elastisk_deformasjon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elastisk_deformasjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Elastisk deformasjon</span> </div> </a> <ul id="toc-Elastisk_deformasjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plastisk_deformasjon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Plastisk_deformasjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Plastisk deformasjon</span> </div> </a> <ul id="toc-Plastisk_deformasjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Brudd" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Brudd"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Brudd</span> </div> </a> <ul id="toc-Brudd-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Matematisk_definisjon" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Matematisk_definisjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Matematisk definisjon</span> </div> </a> <ul id="toc-Matematisk_definisjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tøyning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tøyning"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Tøyning</span> </div> </a> <button aria-controls="toc-Tøyning-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Tøyning</span> </button> <ul id="toc-Tøyning-sublist" class="vector-toc-list"> <li id="toc-Tøyningstensorer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tøyningstensorer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Tøyningstensorer</span> </div> </a> <ul id="toc-Tøyningstensorer-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Litteratur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Litteratur"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Litteratur</span> </div> </a> <ul id="toc-Litteratur-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Innhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Innholdsfortegnelse" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vis/skjul innholdsfortegnelsen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vis/skjul innholdsfortegnelsen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Deformasjon</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå til en artikkel på et annet språk. Tilgjengelig på 55 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-55" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">55 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Deformasjon" title="Deformasjon – norsk nynorsk" lang="nn" hreflang="nn" data-title="Deformasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Deformation" title="Deformation – svensk" lang="sv" hreflang="sv" data-title="Deformation" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Vervorming" title="Vervorming – afrikaans" lang="af" hreflang="af" data-title="Vervorming" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D9%81%D8%B9%D8%A7%D9%84_(%D8%B9%D9%84%D9%85_%D8%A7%D9%84%D9%85%D9%88%D8%A7%D8%AF)" title="انفعال (علم المواد) – arabisk" lang="ar" hreflang="ar" data-title="انفعال (علم المواد)" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Deformaci%C3%B3n" title="Deformación – asturisk" lang="ast" hreflang="ast" data-title="Deformación" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Deformasiya" title="Deformasiya – aserbajdsjansk" lang="az" hreflang="az" data-title="Deformasiya" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A7%82%E0%A6%AA%E0%A6%AC%E0%A6%BF%E0%A6%95%E0%A6%BE%E0%A6%B0_(%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A5%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8)" title="রূপবিকার (পদার্থবিজ্ঞান) – bengali" lang="bn" hreflang="bn" data-title="রূপবিকার (পদার্থবিজ্ঞান)" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%8D%D1%84%D0%B0%D1%80%D0%BC%D0%B0%D1%86%D1%8B%D1%8F" title="Дэфармацыя – belarusisk" lang="be" hreflang="be" data-title="Дэфармацыя" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%94%D1%8D%D1%84%D0%B0%D1%80%D0%BC%D0%B0%D1%86%D1%8B%D1%8F" title="Дэфармацыя – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Дэфармацыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%8F" title="Деформация – bulgarsk" lang="bg" hreflang="bg" data-title="Деформация" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Deformacija_(mehanika)" title="Deformacija (mehanika) – bosnisk" lang="bs" hreflang="bs" data-title="Deformacija (mehanika)" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Deformaci%C3%B3" title="Deformació – katalansk" lang="ca" hreflang="ca" data-title="Deformació" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8" title="Деформаци – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Деформаци" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Deformace" title="Deformace – tsjekkisk" lang="cs" hreflang="cs" data-title="Deformace" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Verformung" title="Verformung – tysk" lang="de" hreflang="de" data-title="Verformung" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%81%CE%B1%CE%BC%CF%8C%CF%81%CF%86%CF%89%CF%83%CE%B7_(%CE%BC%CE%B7%CF%87%CE%B1%CE%BD%CE%B9%CE%BA%CE%AE)" title="Παραμόρφωση (μηχανική) – gresk" lang="el" hreflang="el" data-title="Παραμόρφωση (μηχανική)" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Deformation_(physics)" title="Deformation (physics) – engelsk" lang="en" hreflang="en" data-title="Deformation (physics)" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Deformaci%C3%B3n" title="Deformación – spansk" lang="es" hreflang="es" data-title="Deformación" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Deformi%C4%9Do" title="Deformiĝo – esperanto" lang="eo" hreflang="eo" data-title="Deformiĝo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Deformazio" title="Deformazio – baskisk" lang="eu" hreflang="eu" data-title="Deformazio" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%BA%DB%8C%DB%8C%D8%B1_%D8%B4%DA%A9%D9%84_(%D9%81%DB%8C%D8%B2%DB%8C%DA%A9)" title="تغییر شکل (فیزیک) – persisk" lang="fa" hreflang="fa" data-title="تغییر شکل (فیزیک)" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9formation_d%27un_mat%C3%A9riau" title="Déformation d'un matériau – fransk" lang="fr" hreflang="fr" data-title="Déformation d'un matériau" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Deformaci%C3%B3n" title="Deformación – galisisk" lang="gl" hreflang="gl" data-title="Deformación" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%BC%EA%B7%B8%EB%9F%AC%EC%A7%90_(%EB%AC%BC%EB%A6%AC%ED%95%99)" title="일그러짐 (물리학) – koreansk" lang="ko" hreflang="ko" data-title="일그러짐 (물리학)" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%A5%D6%86%D5%B8%D6%80%D5%B4%D5%A1%D6%81%D5%AB%D5%A1" title="Դեֆորմացիա – armensk" lang="hy" hreflang="hy" data-title="Դեֆորմացիա" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B0%E0%A5%82%E0%A4%AA%E0%A4%A3_(%E0%A4%AF%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80)" title="विरूपण (यांत्रिकी) – hindi" lang="hi" hreflang="hi" data-title="विरूपण (यांत्रिकी)" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Deformacija" title="Deformacija – kroatisk" lang="hr" hreflang="hr" data-title="Deformacija" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Deformasi_(fisika)" title="Deformasi (fisika) – indonesisk" lang="id" hreflang="id" data-title="Deformasi (fisika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Deformazione" title="Deformazione – italiensk" lang="it" hreflang="it" data-title="Deformazione" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%95%D7%95%D7%AA" title="מעוות – hebraisk" lang="he" hreflang="he" data-title="מעוות" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%95%E0%B3%83%E0%B2%A4%E0%B2%BF" title="ವಿಕೃತಿ – kannada" lang="kn" hreflang="kn" data-title="ವಿಕೃತಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%94%E1%83%A4%E1%83%9D%E1%83%A0%E1%83%9B%E1%83%90%E1%83%AA%E1%83%98%E1%83%90" title="დეფორმაცია – georgisk" lang="ka" hreflang="ka" data-title="დეფორმაცია" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%8F" title="Деформация – kasakhisk" lang="kk" hreflang="kk" data-title="Деформация" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%8F_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0%D0%B4%D0%B0)" title="Деформация (физикада) – kirgisisk" lang="ky" hreflang="ky" data-title="Деформация (физикада)" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Deformatio" title="Deformatio – latin" lang="la" hreflang="la" data-title="Deformatio" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Deform%C4%81cija" title="Deformācija – latvisk" lang="lv" hreflang="lv" data-title="Deformācija" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/K%C5%ABno_deformacija" title="Kūno deformacija – litauisk" lang="lt" hreflang="lt" data-title="Kūno deformacija" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86" title="Деформац – mongolsk" lang="mn" hreflang="mn" data-title="Деформац" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Deformatie_(natuurkunde)" title="Deformatie (natuurkunde) – nederlandsk" lang="nl" hreflang="nl" data-title="Deformatie (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%89%E5%BD%A2" title="変形 – japansk" lang="ja" hreflang="ja" data-title="変形" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Deformatsiya" title="Deformatsiya – usbekisk" lang="uz" hreflang="uz" data-title="Deformatsiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Odkszta%C5%82cenie" title="Odkształcenie – polsk" lang="pl" hreflang="pl" data-title="Odkształcenie" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Deforma%C3%A7%C3%A3o" title="Deformação – portugisisk" lang="pt" hreflang="pt" data-title="Deformação" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Deformare" title="Deformare – rumensk" lang="ro" hreflang="ro" data-title="Deformare" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%8F" title="Деформация – russisk" lang="ru" hreflang="ru" data-title="Деформация" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Deformimi_(fizik%C3%AB)" title="Deformimi (fizikë) – albansk" lang="sq" hreflang="sq" data-title="Deformimi (fizikë)" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Deformation" title="Deformation – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Deformation" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Deform%C3%A1cia_(mechanika)" title="Deformácia (mechanika) – slovakisk" lang="sk" hreflang="sk" data-title="Deformácia (mechanika)" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Деформација – serbisk" lang="sr" hreflang="sr" data-title="Деформација" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Deformacija_(mehanika)" title="Deformacija (mehanika) – serbokroatisk" lang="sh" hreflang="sh" data-title="Deformacija (mehanika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Venym%C3%A4" title="Venymä – finsk" lang="fi" hreflang="fi" data-title="Venymä" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B5%E0%B8%A2%E0%B8%94_(%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="ความเครียด (กลศาสตร์) – thai" lang="th" hreflang="th" data-title="ความเครียด (กลศาสตร์)" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C5%9Eekil_de%C4%9Fi%C5%9Ftirme" title="Şekil değiştirme – tyrkisk" lang="tr" hreflang="tr" data-title="Şekil değiştirme" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B5%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D1%96%D1%8F" title="Деформація – ukrainsk" lang="uk" hreflang="uk" data-title="Деформація" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Deformasion" title="Deformasion – venetiansk" lang="vec" hreflang="vec" data-title="Deformasion" data-language-autonym="Vèneto" data-language-local-name="venetiansk" class="interlanguage-link-target"><span>Vèneto</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q193514#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Deformasjon" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskusjon:Deformasjon&action=edit&redlink=1" rel="discussion" class="new" title="Diskusjon om innholdssiden (ikke skrevet ennå) [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Bytt språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">norsk bokmål</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visninger"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Deformasjon"><span>Les</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Deformasjon&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Deformasjon&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Deformasjon&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-dropdown" class="vector-dropdown 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data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Deformasjon"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Deformasjon&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Deformasjon&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Deformasjon&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Deformasjon" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Deformasjon" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=no" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Deformasjon&oldid=24602375" title="Permanent lenke til denne versjonen av siden"><span>Permanent lenke</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Deformasjon&action=info" title="Mer informasjon om denne siden"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siteringshjelp&page=Deformasjon&id=24602375&wpFormIdentifier=titleform" title="Informasjon om hvordan denne siden kan siteres"><span>Siter denne siden</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FDeformasjon"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FDeformasjon"><span>Last ned QR-kode</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Skriv ut / eksporter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesial:DownloadAsPdf&page=Deformasjon&action=show-download-screen"><span>Last ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Deformasjon&printable=yes" title="Utskriftsvennlig versjon av denne siden [p]" accesskey="p"><span>Utskriftsvennlig versjon</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andre prosjekter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Deformation" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q193514" title="Lenke til koblet dataregisterelement [g]" accesskey="g"><span>Wikidata-element</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopedi</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nb" dir="ltr"><p><b>Deformasjon</b> eller <b>deformering</b> er endring i form forårsaket av ytre påvirkning, for eksempel en tilført <a href="/wiki/Kraft" title="Kraft">kraft</a>, eller et for eksempel et temperaturfelt. Deformasjon kan være <i>elastisk</i> eller <i>plastisk</i>, eller en kombinasjon av begge. En tilstrekkelig stor deformasjon fører til <i>brudd</i>. For sprø materialer (for eksempel glass) vil denne skje nokså momentant. Ofte vil en deformasjon være en kombinasjon, men slik at den ene typen er så dominerende at man kun betrakter den dominerende typen. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Typer_deformasjon">Typer deformasjon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=1" title="Rediger avsnitt: Typer deformasjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=1" title="Rediger kildekoden til seksjonen Typer deformasjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Elastisk_deformasjon">Elastisk deformasjon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=2" title="Rediger avsnitt: Elastisk deformasjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=2" title="Rediger kildekoden til seksjonen Elastisk deformasjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elastisk deformasjon er den type deformasjon et materiale utsettes for uten å få varig endring av form. Etter at belastningen er fjernet, vil den elastiske deformasjonen reverseres og materialet gå tilbake til sin opprinnelige form (ved ren elastisk deformasjon). Dette er i motsetning til plastisk deformasjon hvor materialet får en varig fasongendring. Mengden elastisk deformasjon som et materiale kan utsettes for, er definert av <a href="/wiki/Elastisitetsmodulen" class="mw-redirect" title="Elastisitetsmodulen">elastisitetsmodulen</a>. Se også <a href="/wiki/Hookes_lov" title="Hookes lov">Hookes lov</a>. Når du strekker en strikk, forandrer den form så lenge du holder den i strekk. Slipper du strikken, går den tilbake til sin opprinnelige form. Dette er da en elastisk deformasjon. </p> <div class="mw-heading mw-heading3"><h3 id="Plastisk_deformasjon">Plastisk deformasjon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=3" title="Rediger avsnitt: Plastisk deformasjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=3" title="Rediger kildekoden til seksjonen Plastisk deformasjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Plastisk deformasjon inntreffer når et <a href="/wiki/Materiale" title="Materiale">materiale</a> strekkes over flytegrensen (seige materialer). <a href="/wiki/Spenning_(mekanikk)" title="Spenning (mekanikk)">Spenningene</a> blir så store at det oppstår glidninger mellom atomplanene slik at deformasjonen blir varig (plastisk). Selv om materialet er endret så henger det fortsatt sammen på molekylærnivå. Når man klemmer på leire, forandrer den form permanent. Det er en plastisk deformasjon. </p><p>Dersom et legeme blir utsatt for gjentatte (vekslende) laster, som <i>hver for seg</i> ikke fører til varig deformasjon, men etter et antall lastvekslinger over tid brått fører til varig deformasjon, kalles dette for <i><a href="/wiki/Utmatting" title="Utmatting">utmatting</a></i>. </p> <div class="mw-heading mw-heading3"><h3 id="Brudd">Brudd</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=4" title="Rediger avsnitt: Brudd" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=4" title="Rediger kildekoden til seksjonen Brudd"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Når et materiale belastes over bruddgrensen blir spenningene mellom <a href="/wiki/Molekyl" title="Molekyl">molekylene</a> brutt og de blir dermed varig adskilt. Vi får et skille mellom tidligere sammenhengende flater. Et brudd trenger ikke å bety at flatene er synlig adskilt, men kan også observeres som mikroskopiske sprekkdannelser eller riss. </p> <div class="mw-heading mw-heading2"><h2 id="Matematisk_definisjon">Matematisk definisjon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=5" title="Rediger avsnitt: Matematisk definisjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=5" title="Rediger kildekoden til seksjonen Matematisk definisjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Deformasjonen defineres ved hjelp av et referansepunkt, en startposisjon. Dette kan gis i et tredimensjonalt, <a href="/wiki/Euklidsk_rom" title="Euklidsk rom">kartesisk koordinatsystem</a>. Over tid har legemet en gitt <i>konfigurasjon</i> i forhold til referansepunktet, og alle endringer er i henhold til dette.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>For hvert punkt i legemet er denne konfigurasjonen unikt definert ved en <i>posisjonsvektor</i> <b>x</b>, </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 {\bf {{x}={\begin{bmatrix}x_{1}(t)&&x_{2}(t)&&x_{3}(t)\end{bmatrix}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd /> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd /> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bf {{x}={\begin{bmatrix}x_{1}(t)&&x_{2}(t)&&x_{3}(t)\end{bmatrix}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/767b1262f65a83386ae21863011846fa7b88ea89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.213ex; height:2.843ex;" alt="{\displaystyle {\bf {{x}={\begin{bmatrix}x_{1}(t)&&x_{2}(t)&&x_{3}(t)\end{bmatrix}}}}}"></span></dd></dl> <p>som gir posisjon i x-, y- og z-retning og varierer over tid. For ethvert tidspunkt <i>t</i> er <b>x</b> gitt i forhold til en startposisjon <b>X</b>, </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 {\bf {{X}={\begin{bmatrix}X_{1}&&X_{2}&&X_{3}\end{bmatrix}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bf {{X}={\begin{bmatrix}X_{1}&&X_{2}&&X_{3}\end{bmatrix}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac3d52fef020be025b93b3ea634009cf825b4f03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.658ex; height:2.843ex;" alt="{\displaystyle {\bf {{X}={\begin{bmatrix}X_{1}&&X_{2}&&X_{3}\end{bmatrix}}}}}"></span>.</dd></dl> <p>For et gitt punkt vil <b>x</b> definere en <a href="/wiki/Kurve" title="Kurve">kurve</a> (eller en <a href="/w/index.php?title=Trajektorie&action=edit&redlink=1" class="new" title="Trajektorie (ikke skrevet ennå)">trajektorie</a>) i rommet. For et gitt tidspunkt vil posisjonsvektoren til samtlige punkter fullstendig definere legemets konfigurasjon.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><i>Deformasjonsgradienten</i> i et materiale er definert ved en tensor som fullstendig beskriver endringen i ethvert punkt ved et gitt tidspunkt, i forhold til referansevektoren <b>X</b>. Hver komponent er, for en gitt <i>t</i>, definert som<sup id="cite_ref-hol71_3-0" class="reference"><a href="#cite_note-hol71-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </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 F_{ij}={\frac {\partial x_{i}}{\partial X_{j}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{ij}={\frac {\partial x_{i}}{\partial X_{j}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/630752cf38f1040680a85e26783946601951d26f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.058ex; height:6.176ex;" alt="{\displaystyle F_{ij}={\frac {\partial x_{i}}{\partial X_{j}}}}"></span></dd></dl> <p>hvilket tilsammen gir tensoren </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 {\bf {{F}={\begin{bmatrix}{\frac {\partial x_{1}}{\partial X_{1}}}&&{\frac {\partial x_{1}}{\partial X_{2}}}&&{\frac {\partial x_{1}}{\partial X_{3}}}\\{\frac {\partial x_{2}}{\partial X_{1}}}&&{\frac {\partial x_{2}}{\partial X_{2}}}&&{\frac {\partial x_{2}}{\partial X_{3}}}\\{\frac {\partial x_{3}}{\partial X_{1}}}&&{\frac {\partial x_{3}}{\partial X_{2}}}&&{\frac {\partial x_{3}}{\partial X_{3}}}\end{bmatrix}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bf {{F}={\begin{bmatrix}{\frac {\partial x_{1}}{\partial X_{1}}}&&{\frac {\partial x_{1}}{\partial X_{2}}}&&{\frac {\partial x_{1}}{\partial X_{3}}}\\{\frac {\partial x_{2}}{\partial X_{1}}}&&{\frac {\partial x_{2}}{\partial X_{2}}}&&{\frac {\partial x_{2}}{\partial X_{3}}}\\{\frac {\partial x_{3}}{\partial X_{1}}}&&{\frac {\partial x_{3}}{\partial X_{2}}}&&{\frac {\partial x_{3}}{\partial X_{3}}}\end{bmatrix}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0126e0ffd872243b2d148dbb11e16c978c2316" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.263ex; margin-bottom: -0.242ex; width:30.074ex; height:14.176ex;" alt="{\displaystyle {\bf {{F}={\begin{bmatrix}{\frac {\partial x_{1}}{\partial X_{1}}}&&{\frac {\partial x_{1}}{\partial X_{2}}}&&{\frac {\partial x_{1}}{\partial X_{3}}}\\{\frac {\partial x_{2}}{\partial X_{1}}}&&{\frac {\partial x_{2}}{\partial X_{2}}}&&{\frac {\partial x_{2}}{\partial X_{3}}}\\{\frac {\partial x_{3}}{\partial X_{1}}}&&{\frac {\partial x_{3}}{\partial X_{2}}}&&{\frac {\partial x_{3}}{\partial X_{3}}}\end{bmatrix}}}}}"></span></dd></dl> <p>Deformasjonsgradienten er definert for ethvert tidspunkt <i>t</i> og beskriver bevegelsen rundt et punkt på dette tidspunktet.<sup id="cite_ref-hol71_3-1" class="reference"><a href="#cite_note-hol71-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Posisjonen <b>u</b> til ethvert punkt er gitt ved </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 {\bf {{u}={\bf {{x}-{\bf {X}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo mathvariant="bold">−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bf {{u}={\bf {{x}-{\bf {X}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a172799d44df7632c5a54860b5f0cab2c6c4ecfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.393ex; height:2.176ex;" alt="{\displaystyle {\bf {{u}={\bf {{x}-{\bf {X}}}}}}}"></span></dd></dl> <p>og deformasjonsgradienten kan derfor også uttrykkes som<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </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 {\bf {{F}={\bf {{I}+{\frac {\partial {\bf {u}}}{\partial {\bf {X}}}}={\begin{bmatrix}1+u_{11}&&u_{12}&&u_{13}\\u_{21}&&1+u_{22}&&u_{23}\\u_{31}&&u_{32}&&1+u_{33}\end{bmatrix}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mo mathvariant="bold">+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>13</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <mn>1</mn> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>22</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>23</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>31</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>32</mn> </mrow> </msub> </mtd> <mtd /> <mtd> <mn>1</mn> <mo>+</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>33</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bf {{F}={\bf {{I}+{\frac {\partial {\bf {u}}}{\partial {\bf {X}}}}={\begin{bmatrix}1+u_{11}&&u_{12}&&u_{13}\\u_{21}&&1+u_{22}&&u_{23}\\u_{31}&&u_{32}&&1+u_{33}\end{bmatrix}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb8691402fef88422aca157410ae03963376a5ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:51.485ex; height:9.176ex;" alt="{\displaystyle {\bf {{F}={\bf {{I}+{\frac {\partial {\bf {u}}}{\partial {\bf {X}}}}={\begin{bmatrix}1+u_{11}&&u_{12}&&u_{13}\\u_{21}&&1+u_{22}&&u_{23}\\u_{31}&&u_{32}&&1+u_{33}\end{bmatrix}}}}}}}"></span></dd></dl> <p>der <b>I</b> er <a href="/wiki/Identitetsmatrise" title="Identitetsmatrise">identitetsmatrisen</a>. </p><p>Dette kan man også snu og definere som </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 {\text{Grad}}{\bf {{U}={\bf {{F}-{\bf {I}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Grad</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">U</mi> </mrow> <mo mathvariant="bold">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo mathvariant="bold">−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Grad}}{\bf {{U}={\bf {{F}-{\bf {I}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56bf653a16693f55d5f023e0c841c45c7140fee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.422ex; height:2.176ex;" alt="{\displaystyle {\text{Grad}}{\bf {{U}={\bf {{F}-{\bf {I}}}}}}}"></span>,</dd></dl> <p>som er kalt <i>deformasjonsgradienttensoren</i>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Tøyning"><span id="T.C3.B8yning"></span>Tøyning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=6" title="Rediger avsnitt: Tøyning" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=6" title="Rediger kildekoden til seksjonen Tøyning"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relativ deformasjon kalles <i>tøyning</i>. Det er en geometrisk, dimensjonsløs størrelse. Tøyning måler forskyvningen mellom to punkter innenfor et legeme og uttrykkes gjerne som en matematisk fraksjon (brøk/prosentandel) eller på <a href="/wiki/Vektor_(matematikk)" title="Vektor (matematikk)">vektorform</a>. Man bruker også <a href="/wiki/Matrise" title="Matrise">matriser</a> eller <a href="/wiki/Polarkoordinatsystem" title="Polarkoordinatsystem">polar form</a> for å uttrykke tøyning. Relasjonen mellom <a href="/wiki/Spenning_(mekanikk)" title="Spenning (mekanikk)">spenning</a> som en funksjon av tøyning og <a href="/wiki/Elastisitetsmodul" title="Elastisitetsmodul">elastisitetsmodul</a> er uttrykt ved <a href="/wiki/Hookes_lov" title="Hookes lov">Hookes lov</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Tøyningstensorer"><span id="T.C3.B8yningstensorer"></span>Tøyningstensorer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=7" title="Rediger avsnitt: Tøyningstensorer" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=7" title="Rediger kildekoden til seksjonen Tøyningstensorer"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=8" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=8" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><a href="#Hol">Holzapfel: <i>Nonlinear Solid Mechanics</i>, s. 57</a></span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text"><a href="#Hol">Holzapfel: <i>Nonlinear Solid Mechanics</i>, s. 58–59</a></span> </li> <li id="cite_note-hol71-3"><b>^</b> <a href="#cite_ref-hol71_3-0"><sup>a</sup></a> <a href="#cite_ref-hol71_3-1"><sup>b</sup></a> <span class="reference-text"><a href="#Hol">Holzapfel: <i>Nonlinear Solid Mechanics</i>, s. 71</a></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><cite class="citation web">Bob McGinty. <a rel="nofollow" class="external text" href="http://www.continuummechanics.org/deformationgradient.html">«Deformation Gradient»</a><span class="reference-accessdate">. Besøkt 2. januar 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3ADeformasjon&rft.au=Bob+McGinty&rft.btitle=Deformation+Gradient&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.continuummechanics.org%2Fdeformationgradient.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><a href="#Hol">Holzapfel: <i>Nonlinear Solid Mechanics</i>, s. 73</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Litteratur">Litteratur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Deformasjon&veaction=edit&section=9" title="Rediger avsnitt: Litteratur" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Deformasjon&action=edit&section=9" title="Rediger kildekoden til seksjonen Litteratur"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="Hol" class="citation book">Gerhard A. Holzapfel (2000). <i>Nonlinar Solid Mechanics – A Continuum Approach for Engineers</i>. Chichester: John Wiley & Sons. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/978-0471-82304-9" title="Spesial:Bokkilder/978-0471-82304-9">978-0471-82304-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3ADeformasjon&rft.au=Gerhard+A.+Holzapfel&rft.btitle=Nonlinar+Solid+Mechanics+%E2%80%93+A+Continuum+Approach+for+Engineers&rft.date=2000&rft.genre=book&rft.isbn=978-0471-82304-9&rft.place=Chichester&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <p><br /> <style data-mw-deduplicate="TemplateStyles:r24790658">.mw-parser-output .spire{clear:both;border:1px solid var(--border-color-base,#a2a9b1);border-radius:2px;padding:0.325rem;padding-left:3rem;margin:0.5rem 0;font-size:0.8125rem;background-color:var(--background-color-neutral-subtle,#f8f9fa);background-image:url("https://upload.wikimedia.org/wikipedia/commons/2/2d/Stub_W.svg"),url("https://upload.wikimedia.org/wikipedia/commons/c/ce/Emojione_1F331.svg"),url("https://upload.wikimedia.org/wikipedia/commons/7/7a/Grass_compartment.svg");background-repeat:no-repeat;background-position:0.5rem center,bottom right 0.5rem,bottom -2.1rem right -4rem;background-size:2rem,1.8rem,10rem;padding-right:3rem;text-align:start}</style> </p> <div class="spire plainlinks">Denne artikkelen er en <b><a href="/wiki/Wikipedia:Spire" title="Wikipedia:Spire">spire</a></b>. 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Deformasjon – Wikipedia