单晶铁电体的宏细观本构关系描述

以高技术电子材料——铁电单晶体为研究对象，在对铁电体中电畴内的细观力电耦合场分析的基础上，采用Mori-Tanaka方法以自洽的方式导出了材料构元的Helmholtz自由能及Gibbs自由能函数的解析表达式。并分别在广义应力空间和广义应变空间中，按Hil-Rice内变量本构理论框架，导出了铁电体畴变屈服面方程，增量型本构关系及内变量的演化方程。文末给出了对BaTiO₃单晶材料力电行为的一维数值模拟并作了讨论．这里所得到的非线性本构关系，发展了传统的线性压电方程，使之能应用于铁电体的非线性性质。

Taking the high-tech electronic material-ferroelectric single crystal as the research object, based on the analysis of the meso-electromechanical coupling field in the ferroelectric domain, Mori-Tanaka method was used to derive the material element Helmholtz free energy and Gibbs free energy function analytic expression. In the generalized stress space and the generalized strain space, according to the constitutive theory framework of Hil-Rice internal variables, the evolution equation of the yielding surface, the incremental constitutive relation and the internal variable of the ferroelectric domain are deduced. A one-dimensional numerical simulation of the BaTiO₃ single crystal material’s electric and electric behavior is given and discussed. The nonlinear constitutive relationship obtained here develops a traditional linear piezoelectric equation that can be applied to the nonlinear behavior of ferroelectrics.