电致伸缩材料非线性力学计算中的几个问题

Some Problems of Nonlinear Mechanics for Electrostrictive Materials

由于电致伸缩材料本构方程的非线性特性,该材料在力学理论计算、材料参数测试中会出现一定的困难.同时,电场体积力在计算与实验中也应纳入考虑范围.文章给出了一种合适的电致伸缩材料的本构方程,并指出电场体积力的表达式取为Maxwell应力较为合适.利用一种简单模型,给出了0阶近似下的2种处理方式(考虑电场体积力与否)的近似解以及一般处理方式下的解析解.利用推导结果得到了这3种不同处理方式下的位移、应力场数值算例.结果表明,应根据不同条件,在具体计算中合理地处理电场非线性效应以及电场体积力才能得到符合实际情况的结果.

It is difficult to give the theoretical calculating and constants measuring for the electrostrictive materials, since the constitutive equations of this kind of materials are nonlinear. In addition, the electric body force should be taken into consideration. In this paper, the proper constitutive equations have been given. And it is suggested that Maxwell stress is suitable for the electric body force. According to the three different treatments, i.e., the two approx- imate solutions of 0 order （electrical body force considered or not） and analytical solution for general case, the gener- al solutions for a simple model are worked out. Finally, several numerical examples of displacement and stress fields are listed in the table. The numerical results reveal that, the electric nonlinear effect and the electric body force should be considered properly according to the different conditions.