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We prove a convergence result for a system coupling two integral equations with a history-dependent variational inequality. More exactly, we consider the variational formulation of a quasistatic contact problem with adhesion. Then we prove the dependence of the weak solution with respect to the data. The proof is based on arguments of variational inequalities, Fréchet spaces and Gronwall inequalities.

Mathematics Subject Classification (2010): 74G25, 74G30, 74M15, 74505.

Keywords: Viscoplastic material, frictionless contact, unilateral constraint, weak solution, finite element, numerical simulations.