Nonlinear electroelastostatics: Incremental equations and stability

In this paper we first provide an overview of the recently formulated nonlinear constitutive framework for the quasi-static response of electroelastic solids and its isotropic specialization. The general theory exhibits a strong nonlinear coupling between electric and mechanical effects. The main part of the paper focuses on the governing equations describing the linearized response of electroelastic solids superimposed on a state of finite deformation in the presence of an electric field for independent incremental changes in the electric displacement and the deformation within the material. The associated incremental changes in the stress and the electric field within the material and the surrounding space and the incremental boundary conditions are derived for mechanically unconstrained and constrained electroelastic solids and in the isotropic specialization. By way of illustration of the incremental theory, we specialize the constitutive law to an electroelastic neo-Hookean material, and consider the stability of a half-space subjected to pure homogeneous deformation in the presence of an applied electric field normal to its surface. We show that stability is crucially dependent on the magnitudes of the electromechanical coupling parameters in the constitutive equation. (C) 2008 Elsevier Ltd. All rights reserved.