Macroscopical non-linear material model for ferroelectric materials inside a hybrid finite element formulation
Macroscopical non-linear material model for ferroelectric materials inside a hybrid finite element formulation
复制标题
混合有限元公式内铁电材料的宏观非线性材料模型
DOI：
10.1016/j.ijsolstr.2011.10.015
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发表时间：
2012
影响因子：
3.6
通讯作者：
M. Kamlah
中科院分区：
文献类型：
--
作者：
Holger Schwaab;H. Grünbichler;P. Supancic;M. Kamlah
提出了一种基于全铁电/铁弹性耦合宏观材料模型的磁滞非线性铁电陶瓷建模新方法。材料行为由一组屈服函数描述，历史依赖性存储在表示剩余极化和剩余应变的内部状态变量中。为了解决机电耦合边值问题，使用了混合有限元公式。在该公式中，电位移可作为节点量（即自由度）使用，它代替电场来确定剩余极化的演变。这自然涉及到机电耦合。通过定制的返回映射算法获得了本构方程的高效积分技术，定义了常微分方程组。由于算法的一些简化，可以计算解析解。自动微分技术用于获得一致的切线算子。总之，这已通过用户元素实现到有限元代码 FEAP 中。这项工作进行了广泛的验证测试，以评估材料模型在纯电气和机械以及耦合和多轴加载条件下的行为。
A new approach for modeling hysteretic non-linear ferroelectric ceramics is presented, based on a fully ferroelectric/ferroelastic coupled macroscopic material model. The material behavior is described by a set of yield functions and the history dependence is stored in internal state variables representing the remanent polarization and the remanent strain. For the solution of the electromechanical coupled boundary value problem, a hybrid finite element formulation is used. Inside this formulation the electric displacement is available as nodal quantity (i.e. degree of freedom) which is used instead of the electric field to determine the evolution of remanent polarization. This involves naturally the electromechanical coupling. A highly efficient integration technique of the constitutive equations, defining a system of ordinary differential equations, is obtained by a customized return mapping algorithm. Due to some simplifications of the algorithm, an analytical solution can be calculated. The automatic differentiation technique is used to obtain the consistent tangent operator. Altogether this has been implemented into the finite element code FEAP via a user element. Extensive verification tests are performed in this work to evaluate the behavior of the material model under pure electrical and mechanical as well as coupled and multi-axial loading conditions.