Return mapping algorithms and consistent tangent operators in ferroelectroelasticity
Return mapping algorithms and consistent tangent operators in ferroelectroelasticity
复制标题
返回铁电弹性中的映射算法和一致的切线算子
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
H. Balke
中科院分区：
文献类型：
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作者：
A. Semenov;Albrecht C. Liskowsky;H. Balke
为一类相当一般的现象速率无关模型的铁电弹性材料的返回映射算法提出。采用C. M. Landis（2002）提出的具有两个内变量（剩余极化矢量和剩余应变张量）的全耦合热动力学一致三维本构模型，对多晶铁电陶瓷的机电滞回效应进行了模拟。回归映射算法基于算子分裂方法，采用最近点投影格式实现本构模型的高效鲁棒整合。通过对返回映射算法进行线性化，得到了一致切算子的封闭形式，并且由于切换判据依赖于内部变量，在一般情况下一致切算子是非对称的。分析了相容正切矩阵对称的条件。通过使用结合力学和电学值的基于热力学的紧凑符号，获得了所接收关系的紧凑性和通用性。两种情况下均考虑了标量势有限元（主要变量：应变和电场）和矢量势有限元（主要变量：应变和电位移）。通过算例验证了算法的准确性和鲁棒性。版权所有©2009 John Wiley & Sons， Ltd
Return mapping algorithms for a rather general class of phenomenological rate‐independent models for ferroelectroelastic materials are presented. The fully coupled thermodynamically consistent three‐dimensional constitutive model with two internal variables (remanent polarization vector and remanent strain tensor) proposed by C. M. Landis in 2002 is used for the simulation of electromechanical hysteresis effects in polycrystalline ferroelectric ceramics. Based on the operator splitting methodology, the return mapping algorithm employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is obtained in closed form by linearizing the return mapping algorithm, and is found to be non‐symmetric in the general case due to the dependence of the switching criterion on internal variables. Conditions that provide the symmetry of the consistent tangent matrix are analyzed. The compactness and generality of the received relations are achieved by means of using the thermodynamically based compact notations combining mechanical and electrical values. Both the cases scalar potential finite element (FE) formulation (primary variables: strain and electric field) and vector potential FE formulation (primary variables: strain and electric displacement) are considered. The accuracy and robustness of the algorithms are assessed through numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.