Numerical homogenisation of an elasto-plastic model-material with large elastic strains: macroscopic yield surfaces and the Eulerian normality rule
Numerical homogenisation of an elasto-plastic model-material with large elastic strains: macroscopic yield surfaces and the Eulerian normality rule
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DOI：
10.1007/s00466-011-0601-x
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发表时间：
2011-11
影响因子：
4.1
通讯作者：
I. Schmidt
中科院分区：
文献类型：
--
作者：
I. Schmidt
本文详细介绍了一种数值技术，用于计算具有给定微观结构的材料对任意规定载荷历史的宏观响应。该方法使用经典概念的均匀化理论结合有限元法，并侧重于计算的宏观屈服面和非弹性应变率。它对变形的大小没有限制，并允许任意组合的应力或应变控制，包括柯西应力的历史处方。该方法是通过分析模型材料，包括一个非线性弹性矩阵与刚性弹塑性夹杂物，表现出宏观关联的弹塑性材料行为与有限的弹性应变。屈服面和塑性流动的方向后，事先有限的简单剪切变形计算为这种材料，并被证明是一致的添加剂分解的欧拉应变率到弹性和塑性部分和适当的正规规则在柯西应力空间的制定;一个新的版本，后者推导出这是有效的任意参考配置。
This article presents the details of a numerical technique for computing the macroscopic response of a material with a given micro-structure to arbitrary prescribed loading histories. The method uses classical concepts of homogenisation theory in combination with the finite element method and focusses on the computation of macroscopic yield surfaces and inelastic strain rates. It places no restrictions on the magnitude of deformation and allows arbitrary combinations of stress- or strain control including the prescription of histories of the Cauchy stress. The method is illustrated by analysing a model material, consisting of a non-linearly elastic matrix with stiff elasto-plastic inclusions, which exhibits macroscopically associative elasto-plastic material behaviour with finite elastic strains. Yield surfaces and the directions of plastic flow after a prior finite simple shear deformation are computed for this material and are shown to be consistent with an additive decomposition of the Eulerian strain rate into elastic and plastic parts and a suitable formulation of the normality rule in Cauchy stress space; a novel version of the latter is derived which is valid for an arbitrary reference configuration.