A phenomenological constitutive theory for polycrystalline ferroelectric ceramics based on orientation distribution functions

A phenomenological constitutive theory for the ferm-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.