Abstract

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 c-axes 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. The resulting constitutive theory is able to reproduce most essential features of ferroelectric and ferroelastic behavior with minimal computational cost and, furthermore, generates stable predictions in contrast to current phenomenological theories in common use.