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Quasistatic frictional contact of a viscoelastic piezoelectric body. (English) Zbl 1078.74036

Summary: We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable foundation. We use a linear electro-viscoelastic constitutive law to model the piezoelectric material, and the normal compliance condition associated to a general friction law to model the contact. We derive a variational formulation for the model which is in a form of a coupled system involving the displacement and electric potential fields. Then we provide the existence of a unique weak solution to the model. The proof is based on the theory of evolutionary variational inequalities and fixed point argument. We also study the behavior of the solution with respect to the contact conditions, and prove a convergence result.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74D05 Linear constitutive equations for materials with memory
74F15 Electromagnetic effects in solid mechanics
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G40 Regularity of solutions of equilibrium problems in solid mechanics
49J40 Variational inequalities
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