Constitutive model and wave propagation in dissipative electroelastic crystals

Abstract

We propose a constitutive model for dissipative ionic crystals within the classical continuum theory of thermoelectroelasticity which includes polarization gradients as independent variables. According to a previous work, dissipation is modeled by suitable evolution equations for a set of internal variables. The compatibility with the second law of thermodynamics is required to obtain the pertinent constitutive equations. The problem is then linearized about an unstrained and unpolarized state, and the nature of dissipative contributions is pointed out. We apply this model to the study of wave propagation by deriving the eigenvector equation for a two-dimensional problem in the quasi-static hypothesis. The dispersion relation of bulk waves is obtained and discussed for crystals with a centrosymmetric structure.