A phenomenological constitutive theory for the ferro-electro-elastic response of polycrystalline ceramics with tetragonal perovskite structure is proposed. The state of a material point is characterized by an intrinsic polarization vector, an infinitesimal deformation tensor, and an internal variable representing the orientation distribution of the ferroelectric domains at that point. A class of convex thermodynamic potentials in terms of these state variables is posited, and constitutive relations within the framework of generalized standard materials are then derived. The functional form of the dissipation is selected in such a way that it effects an order reduction of the constitutive description whereby the infinite-dimensional internal variable is reduced to finite-dimensional internal variables representing polarization and deformation due to ferroelectric switching, preserving at the same time the generalized standard structure of the theory. By way of example, a specific set of constitutive functions is considered. The resulting constitutive relations are able to emulate most essential features of ferroelectric and ferroelastic behavior with minimal computational cost and, furthermore, generate stable predictions in contrast to earlier phenomenological theories.

提出了一种具有钙钛矿结构的多晶陶瓷铁电弹性响应的现象本构理论。物质点的状态的特征在于固有极化矢量，无穷小变形张量和代表该点铁电畴取向分布的内部变量。根据这些状态变量，提出一类凸热力学势，然后推导广义标准材料框架内的本构关系。以这种方式选择耗散的函数形式，使得其影响本构描述的阶数减少，从而将无穷维内部变量减小为代表由于铁电切换导致的极化和变形的有限维内部变量，并保持不变时间的理论的广义标准结构。通过示例的方式，考虑一组特定的本构函数。由此产生的本构关系能够以最小的计算成本来模拟铁电和铁弹性行为的最基本特征，而且，与早期的现象学理论相比，它还能产生稳定的预测。考虑一组特定的本构函数。由此产生的本构关系能够以最小的计算成本来模拟铁电和铁弹性行为的最基本特征，而且，与早期的现象学理论相比，它还能产生稳定的预测。考虑一组特定的本构函数。由此产生的本构关系能够以最小的计算成本来模拟铁电和铁弹性行为的最基本特征，而且，与早期的现象学理论相比，它还能产生稳定的预测。