A piezoelectric contact problem with normal compliance
Volume 32 / 2005
Applicationes Mathematicae 32 (2005), 425-442 MSC: 74M10, 74M15, 49J40, 74M99. DOI: 10.4064/am32-4-5
We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an insulator foundation. We use a nonlinear electroelastic constitutive law to model the piezoelectric material and the normal compliance condition associated to a version of Coulomb's friction law to model the contact. We derive a variational formulation for the model which is in the form of a coupled system involving the displacement and the electric potential fields. Then we provide the existence of a weak solution to the problem and, under a smallness assumption, its uniqueness. We also study the dependence of the solution on the contact conditions and derive a convergence result.