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Existence and approximation of a solution to quasistatic Signorini problem with local friction. (English) Zbl 1210.74126
Summary: We consider an elastic body submitted to a local Coulomb friction law on a part of his boundary. After discretizing the variational formulation with respect to time, we use a smoothing technique to approximate the friction law in an auxiliary problem. A shifting technique enables us to obtain the existence of a solution with bounds independent of the regularization parameter. We prove the existence of a solution for the incremental problem, which is bounded independently of time and we construct a solution of the quasistatic problem by taking the limit of incremental solution.

MSC:
74M10 Friction in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74M15 Contact in solid mechanics
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