Finite Element Simulation of the Non-remanent Straining Ferroelectric Material Behaviour Based on the Electrostatic Scalar Potential:Convergence and Stability
Finite Element Simulation of the Non-remanent Straining Ferroelectric Material Behaviour Based on the Electrostatic Scalar Potential:Convergence and Stability
复制标题
基于静电标量势的非剩磁应变铁电材料行为的有限元模拟：收敛性和稳定性
DOI：
10.1007/978-90-481-9887-0_6
复制
发表时间：
2011
影响因子：
3.6
通讯作者：
H. Balke
中科院分区：
文献类型：
--
作者：
S. Roth;P. Neumeister;A. Semenov;H. Balke
牛顿-拉夫森迭代方案的适用性的一个铁电/铁弹本构模型的框架内的有限元模拟的标量电位制定系统地分析。由于极化滞后的具体形状被认为是数值问题的主要原因，这里给出的考虑仅限于非抑制应变铁电材料模型。三种方法来获得收敛进行了讨论。除了已知的线搜索的其他两种方法，这是局部应用于每个积分点。虽然第一种方法的主要思想是修改内部介电位移的矢量，但第二种方法影响切线模量。一个额外的缩放的切线模量，提出了为了抑制数值不稳定性，可能会出现作为一个过度补偿的数值误差的结果。为了识别回波偏振，使用基于隐式后向欧拉方法的增强回波映射算法。通过两个算例验证了改进的数值迭代方法的适用性。
The applicability of the Newton–Raphson iteration scheme to an electric scalar potential formulation of a ferroelectric/ferroelastic constitutive model within the framework of a finite element simulation is analysed methodically. Since the specific shape of the polarisation hysteresis is recognised as the principal reason of numerical problems, the considerations given here are limited to the non-remanent straining ferroelectric material model. Three approaches to gain convergence are discussed. Besides the known Line Search two other methods are presented, which are applied locally for each integration point. While the main idea of the first is to modify the vector of the internal dielectric displacement, the second approach affects the tangent modulus. An additional scaling of the tangent modulus is proposed in order to suppress numerical instabilities which may arise as a consequence of an over-compensation of numerical errors. To identify the remanent polarisation an enhanced Return Mapping algorithm based on an implicit backward Euler method is used. The applicability of the modified numerical iteration procedure is demonstrated by two examples.