Numerical approximation of incremental infinitesimal gradient plasticity
Numerical approximation of incremental infinitesimal gradient plasticity
复制标题
增量无穷小梯度塑性的数值逼近
DOI：
10.1002/nme.2420
复制
发表时间：
2009
影响因子：
2.9
通讯作者：
C. Wieners
中科院分区：
文献类型：
--
作者：
P. Neff;Antje Sydow;C. Wieners
研究了一个具有代表性的连续体无穷小梯度塑性模型。该公式是基于对称应变张量对弹性和塑性部分的加性分解的经典速率无关的无穷小塑性的扩展。假设位错过程有助于能量在材料中的储存，因此塑性变形的旋度出现在热力学势中，并导致额外的非局部背应力张量。通过对每个增量加载步骤中相应的最小化问题的鞍点近似，将该公式转化为数值框架。这允许人们将（非局部）耗散不等式重新表述为一个点方向的流动规则，并产生一个解决方案，这是经典塑性标准方法的直接扩展。我们的数值结果显示了附加物理激励项的正则化效应。版权所有©2008 John Wiley & Sons， Ltd
We investigate a representative model of continuum infinitesimal gradient plasticity. The formulation is an extension of classical rate‐independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts. It is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor. The formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step. This allows one to reformulate the (nonlocal) dissipation inequality to a point‐wise flow rule and yields a solution scheme, which is a direct extension of the standard approach in classical plasticity. Our numerical results show the regularizing effects of the additional physically motivated terms. Copyright © 2008 John Wiley & Sons, Ltd.