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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:
49J45Optimal control problems involving semicontinuity and convergence; relaxation
49J53Set-valued and variational analysis
74M10Friction (solid mechanics)
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