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Existence of a solution for a quasistatic problem of unilateral contact with local friction. (English. Abridged French version) Zbl 0935.74054
Summary: The existence result in linear elasticity obtained for the quasistatic problem of unilateral contact with regularized Coulomb friction is extended to a local friction problem. After discretizing the implicit variational inequality with respect to time, we have to solve a sequence of variational inequalities similar to ones in the static problem. If the friction coefficient is small enough, we show the existence of incremental solution. We also construct a suitable sequence of functions converging towards a quasistatic solution of the problem.

74M15 Contact in solid mechanics
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74M10 Friction in solid mechanics
74B05 Classical linear elasticity
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