Elastoplasticity with linear tetrahedral elements: A variational multiscale method

Abboud Nabil; Scovazzi Guglielmo

摘要

Summary > We present a computational framework for the simulation of <fi>J</fi> <sub>2</sub> ‐elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid spurious numerical instabilities by means of a specific stabilization method of the variational multiscale kind. Specifically, we introduce the concept of subgrid‐scale displacements, velocities, and pressures, approximated as functions of the governing equation residuals. The subgrid‐scale displacements/velocities are scaled using an effective (tangent) elastoplastic shear modulus, and we demonstrate the beneficial effects of introducing a subgrid‐scale pressure in the plastic regime. We provide proofs of stability and convergence of the proposed algorithms. These methods are initially presented in the context of static computations and then extended to the case of dynamics, where we demonstrate that, in general, na?ve extensions of stabilized methods developed initially for static computations seem not effective. We conclude by proposing a dynamic version of the stabilizing mechanisms, which obviates this problematic issue. In its final form, the proposed approach is simple and efficient, as it requires only minimal additional computational and storage cost with respect to a standard finite element relying on a piecewise linear approximation of the displacement field. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract xmlns =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”xml：id =“nme5831-abs-abs-0001”> <标题类型=“main” >摘要</ title> >我们提出了一种基于简单分段线性有限元的复杂几何形状中的<fi> j </ fi> <sub> 2 </ sub> -elastic /塑料材料的计算框架四面体网格。我们通过特定的多尺度类型的特定稳定方法避免虚假数值不稳定性。具体而言，我们介绍了近似级位移，速度和压力的概念，近似为控制方程式残差的函数。使用有效（切线）弹性剪切模量来缩放子级尺度位移/速度，并且我们证明了在塑料制度中引入底板压力的有益效果。我们提供所提出的算法的稳定性和融合的证据。这些方法最初在静态计算的背景下呈现，然后扩展到动态的情况，在那里，我们证明通常，最初开发静态计算的稳定方法的Na ve延伸似乎没有有效。通过提出稳定机制的动态版本，我们得出结论，这消除了这种有问题的问题。在最终形式中，所提出的方法简单且有效，因为它只需要最小的额外计算和存储成本，而依赖于位移场的分段线性近似的标准有限元。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20801/'>《International Journal for Numerical Methods in Engineering》</a> <b style="margin: 0 2px;">|</b><span>2018年第8期</span><b style="margin: 0 2px;">|</b><span>共43页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abboud Nabil&option=202" target="_blank" rel="nofollow">Abboud Nabil;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Scovazzi Guglielmo&option=202" target="_blank" rel="nofollow">Scovazzi Guglielmo;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Civil &</p> <p>Environmental EngineeringDuke UniversityDurham North Carolina USA;</p> <p>Department of Civil &</p> <p>Environmental EngineeringDuke UniversityDurham North Carolina USA;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/6940.html" title="工程数学">工程数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=finite deformation&option=203" rel="nofollow">finite deformation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=plasticity&option=203" rel="nofollow">plasticity;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=small strains&option=203" rel="nofollow">small strains;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stabilized methods&option=203" rel="nofollow">stabilized methods;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=tetrahedral finite elements&option=203" rel="nofollow">tetrahedral finite elements;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=variational multiscale method&option=203" rel="nofollow">variational multiscale method;</a> </p> <div class="translation"> 机译：有限变形;可塑性;小菌株;稳定的方法;四面体有限元;变分多尺度方法; 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