Nonlinear Constitutive Modeling of Electroelastic Solids

Abstract

In this chapter, the equations governing the mechanical behavior of electroelastic solids capable of finite deformations are summarized with particular reference to the development of constitutive equations describing the electromechanical interactions in soft dielectric materials. Following a brief summary of some background from continuum mechanics and nonlinear elasticity theory, the equations of electrostatics are given in Eulerian form and then re-cast in Lagrangian form. The electroelastic constitutive equations are based on the existence of a so-called total energy function, which may be regarded as a function of the Lagrangian form of either the electric field or electric displacement as the independent electric variable, together with the deformation gradient. For each form of the total energy function, corresponding expressions for the (total) nominal and Cauchy stress tensors are provided, both in full generality and for their isotropic specializations for unconstrained and incompressible materials. The general formulas are then applied to the basic problem of homogeneous deformation of a rectangular plate, and illustrated by the choice of a simple specific example of constitutive equation. As a further illustration, the theory is applied to the analysis of a nonhomogeneous deformation of a circular cylindrical tube subject to an axial force, a torsional moment, and a radial electric field generated by a potential difference between flexible electrodes covering its inner and outer curved surfaces.