Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects
Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects
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DOI：
10.1002/nme.4256
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发表时间：
2012-07
影响因子：
2.9
通讯作者：
S. Bauer;W. Dettmer;Dunja Perić;M. Schäfer
中科院分区：
文献类型：
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作者：
S. Bauer;W. Dettmer;Dunja Perić;M. Schäfer
开发了一种包含各向同性硬化的基于微极超弹性的有限弹塑性计算模型。回顾了非线性微极运动学框架的基本概念，并描述了具有 Neo-Hooke 型弹性和广义 von Mises 塑性的热力学一致本构模型。本构初值问题的积分是通过弹性预测器/塑性校正器算法进行的，该算法保留了塑性不可压缩性。解决方案过程经过仔细开发并详细描述。导出一致的材料切线。微极本构模型在隐式有限元框架中实现。给出了承受大轴向位移和大扭转角的缺口圆柱杆的数值示例。有限元模拟的结果表明（i）该方法能够捕获有限应变状态下三维弹塑性固体的尺寸效应，（ii）该公式在存在应变局部化的情况下具有正则化效果，以及（iii）实现了牛顿-拉夫森过程的渐近二次收敛率。在本文中，我们努力将这些进展呈现为标准有限变形计算塑性的直接扩展。版权所有 © 2012 约翰·威利父子有限公司
A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.