许多物理实验证明了在铁电体材料切换的领域是有应力和电场的变化的领域墙的一个复杂进化过程。根据这机制，切换的领域的体积部分在陶器、使用的铁电体的组成的法律被介绍在这篇论文学习铁电体身体的非线性的组成的行为。静止全部的精力的原则在基本未知数量在哪个是排水量 u i , 电的排水量 D i 并且卷部分 ρ
我 为变体切换的域我。机械领域方程和交换标准的一个新领域从静止全部的精力的原则被获得。切换的标准在这篇论文建议了的域是精力标准的扩大和开发。根据交换标准的领域，为体积部分 ρ
我 领域，切换被获得，在哪个线性代数学的方程的系数仅仅包含未知种类和电场。然后一个单个领域机械模型在这篇论文被建议。poled 铁电体标本被看作一个横着各向同性的单个领域。由使用部分试验性的结果，在域切换和域切换的卷部分的驱动力之间的变硬的关系能被校准。然后，机电的反应能根据校准的变硬的关系被计算。结果包含电的蝴蝶轴的紧张对轴的电场的塑造的曲线，电的排水量的磁滞现象环对电走并且在装载的单轴的联合应力和电场下面在铁电体标本切换的域的进化进程。现在的理论上的预言相当同意，试验性的结果由林奇给。
The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism,a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated,the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material,one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Mean-while,the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation,the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The in-teraction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.
