On weak formulations and their second variation in nonlinear electroelasticity

A variational formulation for an electro-elastic body surrounded by free space in the context of large and nonlinear elastic deformations is developed. The functional depends on the deformation function and the electric scalar potential. The approach presented here introduces an alternative expression for the energy stored by the exterior free space, which is intended to facilitate the (in general troublesome) calculations of the first and the second variations of the functional.