Nonlinear electro-elastic bodies with residual stresses: spectral formulation

Abstract

Abstract In the present article, a spectral model is developed for residually stressed electro-elastic bodies. The model uses a total energy function that depends on the right stretch tensor, residual stress tensor and one of the electric variables. Some boundary value results with cylindrical symmetry are given. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The constitutive formulation contains spectral invariants that have an immediate physical interpretation which is useful in a rigorous construction of a specific form of the total energy function via an appropriate experiment