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Contact models leading to variational-hemivariational inequalities. (English) Zbl 1248.49017
Summary: A frictional contact model, under the small deformations hypothesis, for static processes is considered. We model the behavior of the material by a constitutive law using the subdifferential of a proper, convex and lower semicontinuous function. The contact is described with a boundary condition involving Clarke’s generalized gradient. Our study focuses on the weak solvability of the model. Based on a fixed-point theorem for set-valued mappings, we prove the existence of at least one weak solution. The uniqueness, the boundedness and the stability of the weak solution are also discussed; the investigation is based on arguments in the theory of variational--hemivariational inequalities. Finally, we present several examples of constitutive laws and friction laws for which our theoretical results are valid.

##### MSC:
 49J45 Optimal control problems involving semicontinuity and convergence; relaxation 49J53 Set-valued and variational analysis 74M10 Friction (solid mechanics)
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##### References:
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