A contact problem for electro-elastic materials

We analyze the frictionless unilateral contact between an electro-elastic body and a rigid electrically conductive foundation. On the potential contact zone, we use the Signorini condition with non-zero gap and an electric contact condition with a conductivity depending on the Cauchy vector. We provide a weak variationally consistent formulation and show existence, uniqueness and stability of the solution. Our analysis is based on fixed point techniques for weakly sequentially continuous maps. We conclude by a numerical example that illustrates the applicability of the model.