Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics

In this paper, a general form for multi-axial constitutive laws for ferroelectric ceramics is constructed. The foundation of the theory is an assumed form for the Helmholtz free energy of the material. Switching surfaces and associated flow rules are postulated in a modified stress and electric field space such that a positive dissipation rate during switching is guaranteed. The resulting tangent moduli relating increments of stress and electric field to increments of strain and electric displacement are symmetric since changes in the linear elastic, dielectric and piezoelectric properties of the material are included in the switching surface. Finally, parameters of the model are determined for two uncoupled cases, namely non-remanent straining ferroelectrics and purely ferroelastic switching, and then for the fully coupled ferroelectric case.