A nonlinear constitutive model for some hard electro-elastic solids. Solutions of some boundary value problems

A constitutive equation for a class of electro-elastic solid is proposed, neglecting dissipation of energy, and assuming that the gradient of the displacement field is small (the above implies the strains are small). Using the theory of implicit constitutive relations developed by Rajagopal and co-workers, a constitutive equation is proposed where the linearized strain is a function of the Cauchy stress and the electric field. The polarization field is assumed to be a function of the Cauchy stress and the electric field as well. The material parameters are adjusted to model the behaviour of some ceramic-like materials. Several boundary problems are solved to study the predictions of these new constitutive equations.