A frictional contact problem for an electro-viscoelastic body
A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.
Lerguet Z., Shillor M., and Sofonea M. (2007). A frictional contact problem for an electro-viscoelastic body. Electronic Journal of Differential Equations, 2007(170), 1-16.
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