Micromechanical modeling of switching effects in piezoelectric materials - A robust coupled finite element approach
Micromechanical modeling of switching effects in piezoelectric materials - A robust coupled finite element approach
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DOI：
10.1177/1045389x06074117
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发表时间：
2007-09-01
影响因子：
2.7
通讯作者：
Seemann, Wolfgang
中科院分区：
文献类型：
--
作者：
Arockiarajan, Arunachalakasi;Menzel, Andreas;Seemann, Wolfgang
本文建立了压电材料的微机械驱动模型。特别地，研究了具有四方钙钛矿型亚结构的多晶试样的非线性行为，并阐述了一个鲁棒的三维耦合有限元公式。在提出的模型中考虑了不同取向的晶粒，其中附着在每个晶粒上的代表性偶极子方向是随机取向的。此外，采用适用于单个域的能量减少准则作为域切换过程启动的准则。在此基础上，可以用经典的体积平均技术预测宏观体响应。然而，实际上，即使在经典的临界能垒以下，畴转换也可能发生，这主要是由于所谓的晶间效应。通过将实际能级与临界能级联系起来，通过现象学动机概率方法将这些效应纳入已开发的框架。为了比较有代表性的耦合有限元算例与文献中报道的实验数据，对块状材料施加宏观单轴和准静态载荷：首先，讨论了纯电载荷下的滞回曲线和蝴蝶曲线；其次，对试件施加轴向和侧向附加力学载荷。
A micromechanically motivated model for piezoelectric materials has been developed in this work. In particular, the nonlinear behavior of poly-crystalline specimens with tetragonal perovskite-type substructure are studied, and a robust three-dimensional coupled finite element formulation is elaborated. Differently oriented grains are taken into account within the proposed model, whereby representative dipole directions attached to each grain are randomly oriented. Furthermore, an energy reduction criterion applied to individual domains is adopted as a criterion for the initiation of domain switching processes. Based on this, macroscopic bulk response can be predicted by classical volume-averaging techniques. In practice, however, domain switching might occur even below the classical critical energy barrier which mainly stems from so-called intergranular effects. These effects are incorporated into the developed framework via a phenomenologically motivated probabilistic approach by relating the actual energy level to a critical energy level. In order to compare representative coupled finite element examples with experimental data reported in the literature, macroscopically uni-axial and quasi-static loading is applied to the bulk material: first, hysteresis and butterfly curves under purely electrical loading are discussed; secondly, additional mechanical loads in axial and lateral direction are applied to the specimen.