Abstract

Implicit constitutive relations are proposed for electro-elastic and thermo-electro-elastic solids, which cannot be classified as Cauchy or Green elastic bodies, i.e., where in general it is not assumed that the stresses and one of the electric variables are given as functions (or the derivative of an energy function) in terms of the strains, and the independent electric variable. Some subclasses of the above implicit relations are studied in detail, in particular some constitutive equations that appear in the case the mechanical and electrical behaviour of the body is in general nonlinear, but the strains are assumed to be small (small gradient of the displacement field). The first and second laws of thermodynamics are used to impose restrictions on the above implicit constitutive relations and equations.