Solution for the general integral‐type nonlocal plasticity model with Tikhonov regularization

机译：Tikhonov规范化的通用整体非局部无局部塑性模型解决方案

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Summary >A new solution approach, based on Tikhonov regularization on the Fredholm integral equations of the first kind, is proposed to find the approximate solutions of the strain softening problems. In this approach, the consistency condition is regularized with the Tikhonov stabilizers along with a regularization parameter, and the internal variable increments are solved from the resulting Euler's equations. It is shown that, as the regularization parameter is increased, the solutions converge to a unique one. A nonlocal yield condition and a nonlocal return mapping algorithm are proposed to carry out the integration of constitutive equations in the time and spatial domains. A global plastic dissipation principle is proposed to relax the classical local plastic dissipation postulate. Numerical examples show that the proposed approach leads to objective, mesh‐independent solutions of the softening‐induced localization problems. A comparison of the results from the proposed approach with those from the gradient‐dependent plasticity model shows that the two models give close solutions. </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”> <title type =“main”>摘要</ title> >一个新的提出了基于第一类Fredholm积分方程的Tikhonov正规的解决方案方法，以找到应变软化问题的近似解。在这种方法中，使用Tikhonov稳定器以及正则化参数进行一致性条件，并且内部可变增量从得到的欧拉方程解决。结果表明，随着正则化参数的增加，解决方案会聚到唯一的参数。建议在时间和空间域中执行非局部产量条件和非本体返回映射算法。建议全球塑料耗散原则放宽古典局部塑料耗散假设。数值例子表明，该方法导致客观，近似的软化诱导的本地化问题。从梯度依赖塑性模型中提出的方法的结果与来自梯度依赖性塑性模型的结果的比较表明，这两种型号提供了密切的解决方案。</ p> </摘要> </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7期</span><b style="margin: 0 2px;">|</b><span>共34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=Wu Shouxin&option=202" target="_blank" rel="nofollow">Wu Shouxin;</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>School of Civil EngineeringSouthwest Jiaotong UniversityChengdu China;</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 element&option=203" rel="nofollow">finite element;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Fredholm integral equation&option=203" rel="nofollow">Fredholm integral equation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=mesh dependence&option=203" rel="nofollow">mesh dependence;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=nonlocal plasticity&option=203" rel="nofollow">nonlocal plasticity;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=strain localization&option=203" rel="nofollow">strain localization;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Tikhonov regularization&option=203" rel="nofollow">Tikhonov regularization;</a> </p> <div class="translation"> 机译：有限元;Fredholm积分方程;网格依赖;非局部可塑性;应变定位;Tikhonov规则化; 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