A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting

In this contribution we present a phenomenological mesoscopic thermodynamically consistent model for the description of switching processes in ferroelectric materials that is able to describe the fundamental electromechanical hysteresis effects. The main goal is to develop a representation using the set of independent variables, the strains and the electric field, in a coordinate-invariant setting. This formulation is particularly suitable for the treatment of a variety of complex boundary-value problems (BVP) with regard to the essential boundary conditions. Here we restrict ourselves to transversely isotropic solids. The anisotropic behavior is governed by isotropic tensor functions that depend on a finite set of invariants. Thus the material symmetry requirements are automatically fulfilled.