外加电场作用下层状铁电多晶材料板的模拟

On the Modeling of a Layered Ferroelectric Polycrystalline Plate under an Applied Electric Field

建立了一个模拟在外加电场作用下的层状铁电多晶板的模型．该模型认为铁电材料的能量密度函数是变形和电位移的非凸函数以及引入了畴变对材料行为的影响．为了满足各晶粒间的运动学约束及电位移场的连续性条件，模型认为每个晶粒具有某种混合构形．通过常应力和常电场强度假设及利用加载过程中须满足的连续性条件，该模型将求解板对外加电场的响应问题转化为求解各晶粒中的应力及各晶界上的电位势的代数方程组的问题．同时，该模型利用两电畴的Ｇｉｂｂｓ自由能之差作为畴变的方向的判据，由要求板的Ｇｉｂｂｓ函数最小来确定畴变量的大小．

In this article, the response of a layered ferroelectric polycrystalline plate with a periodic boundary subjected to an applied electric field is simulated. The non-convexity of the energy density of the material is incorporated in the model, and the effect of domain switching is taken into consideration. In order to fulfill the kinematic constraints and the continuity requirement of the electric displacement over the grain boundaries, each grain is considered to have a mixed configuration, i.e., the grains generally consist of more than one domain. In this model, the stress and electric fields are assumed to be constant in all grains, and the domain switching between two domains is governed by the difference between the Gibbs free energies associated with these two domains.