Constitutive relations and their time integration for anisotropic elasto-plastic porous materials
Constitutive relations and their time integration for anisotropic elasto-plastic porous materials
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DOI：
10.1016/j.cma.2016.06.005
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发表时间：
2016-10
影响因子：
7.2
通讯作者：
S. Kweon;B. Sagsoy;A. Benzerga
中科院分区：
文献类型：
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作者：
S. Kweon;B. Sagsoy;A. Benzerga
针对一类微观结构演化的塑性各向异性多孔固体，建立了有限变形本构关系。它们是基于刚性理想塑性材料含有非球形空隙均匀化得到的模型。为了便于数值实现，提出了启发式扩展，将弱弹性，应变硬化和准确的空洞形状的演变。采用半隐式时间积分方法，沿着采用Newton-Raphson方法求解本构方程离散化后的方程组。总结了求解整体力-位移矩阵方程所需的一致切线矩阵的计算过程。该框架被用来说明该模型的预测能力，首先在以前评估的条件下对有限元单元模型计算，然后在迄今为止没有检查的条件下。后者包括初始各向异性的情况，以及涉及显着的空隙扭曲的情况下，不仅在空隙扩大或形状变化，但也在空隙旋转。特别是，各种组合的应力三轴度，初始空隙形状，空隙方向，矩阵正交各向异性性能和加载方向进行了模拟。此外，该模型的有限元实现解决和说明简单的情况下。
Finite deformation constitutive relations are developed for a class of plastically anisotropic porous solids with an underlying evolving microstructure. They are based on a model obtained by homogenization for rigid-perfectly plastic materials containing non-spherical voids. To facilitate numerical implementation, heuristic extensions are proposed to incorporate weak elasticity, strain hardening and accurate void shape evolution. A semi-implicit time integration scheme is used along with the Newton–Raphson method to solve the system of equations resulting from the discretization of the constitutive equations. The procedure to calculate the consistent tangent matrix, which is needed to solve the global force–displacement matrix equation, is summarized. The framework is used to illustrate the predictive capabilities of the model, first under conditions previously assessed against finite element cell model calculations, then under conditions heretofore not examined. The latter include situations of initial anisotropy as well as situations involving significant void distortions, not only in terms of void enlargement or shape change, but also in terms of void rotations. In particular, various combinations of stress triaxiality, initial void shape, void orientation, matrix orthotropy properties and loading directions are simulated. In addition, the finite element implementation of the model is addressed and illustrated for simple cases.