Abstract

An integral identity is constructed from properties of the energy momentum tensor and is used to demonstrate uniqueness of the displacement on star-shaped regions to the afine boundary value problem of the nonlinear homogeneous elastic dielectric. The method of proof, nontrivially adapted from that of the corresponding elastic problem, assumes the electric enthalpy function to be rank-one convex and strictly quasiconvex. Furthermore, for a given displacement gradient, the electric quantities are proved unique for specified nonafine and nonuniform electric boundary conditions subject to the electric enthalpy and strain energy functions satisfying additional convexity conditions.

Keywords

elastic dielectric, affine boundary values, uniqueness

Authors