Hemivariational inequalities modeling electro-elastic unilateral frictional contact problem. (English) Zbl 1451.74178
Summary: We study a class of abstract hemivariational inequalities in a reflexive Banach space. For this class, using the theory of multivalued pseudomonotone mappings and a fixed-point argument, we provide a result on the existence and uniqueness of the solution. Next, we investigate a static frictional contact problem with unilateral constraints between a piezoelastic body and a conductive foundation. The contact, friction and electrical conductivity condition on the contact surface are described with the Clarke generalized subgradient multivalued boundary relations. We derive the variational formulation of the contact problem which is a coupled system of two hemivariational inequalities. Finally, for such system we apply our abstract result and prove its unique weak solvability.
MSC:
| 74M15 | Contact in solid mechanics |
| 74M10 | Friction in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74G22 | Existence of solutions of equilibrium problems in solid mechanics |
| 74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
| 49J40 | Variational inequalities |
Keywords:
hemivariational inequality; Clarke generalized subgradient; piezoelectric material; normal compliance; unilateral constraint; non-monotone frictionReferences:
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