Document Zbl 1548.74703

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J. Numer. Methods Eng.</a> <a href="/?q=in%3A371577" title="Articles in this Issue">112, No. 7, 803-831 (2017)</a>. </div> <div class="abstract">Summary: The numerical manifold method (NMM) builds up a unified framework that is used to describe continuous and discontinuous problems; it is an attractive method for simulating a cracking phenomenon. Taking into account the differences between the generalized degrees of freedom of the physical patch and nodal displacement of the element in the NMM, a decomposition technique of generalized degrees of freedom is deduced for mixed mode crack problems. An analytic expression of the energy release rate, which is caused by a virtual crack extension technique, is proposed. The necessity of using a symmetric mesh is demonstrated in detail by analysing an additional error that had previously been overlooked. Because of this necessity, the local mathematical cover refinement is further applied. Finally, four comparison tests are given to illustrate the validity and practicality of the proposed method. The aforementioned aspects are all implemented in the high-order NMM, so this study can be regarded as the development of the virtual crack extension technique and can also be seen as a prelude to an h-version high-order NMM.<br class="zbmathjax-paragraph">{Copyright © 2017 John Wiley & Sons, Ltd.}</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7867232">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74R10" title="MSC2020">74R10</a> </td> <td class="space"> Brittle fracture </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anumerical+manifold+method">numerical manifold method</a>; <a href="/?q=ut%3Avirtual+crack+extension">virtual crack extension</a>; <a href="/?q=ut%3Aenergy+release+rate">energy release rate</a>; <a href="/?q=ut%3Adecomposition+of+generalized+degrees+of+freedom">decomposition of generalized degrees of freedom</a>; <a href="/?q=ut%3Amathematical+cover+refinement">mathematical cover refinement</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1548.74703" data-ciurl="/ci/07867232" data-biburl="/bibtex/07867232.bib" data-amsurl="/amsrefs/07867232.bib" data-xmlurl="/xml/07867232.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07867232.pdf" title="Zbl 1548.74703 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/nme.5533" aria-label="DOI for “A decomposition technique of generalized degrees of freedom for mixedmode crack problems”" title="10.1002/nme.5533">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Irwin, GR, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, 24, 361-364, 1957</td> </tr><tr> <td>[2]</td> <td class="space">Griffith, AA, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, A211, 163-198, 1921 · <a href="/1454.74137" class="nowrap">Zbl 1454.74137</a></td> </tr><tr> <td>[3]</td> <td class="space">Rice, JR, A path independent integral and the approximation analysis of strain concentration by notches and cracks, Journal of Applied Mechanics, 35, 379-386, 1968</td> </tr><tr> <td>[4]</td> <td class="space">Chan, SK; 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