Variational analysis of fully coupled electro-elastic frictional contact problems (Q2786308)

The paper contains a short description of the piezoelectric phenomenon, states some piezoelectric materials, and develops a theory of contact mechanics. More precisely, a mathematical model is established describing the static frictional contact between a piezoelectric body and a foundation. The material behavior is described by a nonlinear electro-elastic constitutive law. The novelty of the model lies in the fact that the foundation is assumed to be electrically conductive, and that the frictional contact and the contact surface are characterized by sub-differential boundary conditions involving a full coupling between mechanical and electrical variables. A variational formulation of the problem leads to the coupling of two hemivariational inequalities for the displacement and electric potential fields, respectively. An existence proof for a weak solution to the mathematical model is given, and its uniqueness is obtained under additional assumptions. The proofs are based on recent results for inclusions of sub-differential type in Sobolev spaces.