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A piezoelectric contact problem with slip-dependent coefficient of friction. (English) Zbl 1092.74029

Summary: We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled by a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is a coupled system involving as unknowns the displacement field and electric potential. Then we prove the existence of weak solution and, under a smallness assumption, we prove its uniqueness. The proof is based on a result obtained by D. Montreanu and M. Sofonea [Adv. Math. Sci. Appl. 10, 103–118 (2000)] in the study of elliptic quasi-variational inequalities.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
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