Analysis of a history-dependent frictional contact problem |
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Authors: | M. Sofonea A. Farcaş |
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Affiliation: | 1. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue de Paul Alduy, 66 860 Perpignan, France.sofonea@univ-perp.fr;3. Faculty of Mathematics and Computer Science, Babe?-Bolyai University, Kog?lniceanu Street No. 1, 400084 Cluj-Napoca, Romania. |
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Abstract: | We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and a foundation. The material’s behaviour is modelled with a constitutive law with long memory. The contact is frictional and is modelled with normal compliance and memory term, associated to the Coulomb’s law of dry friction. We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove the unique weak solvability of the problem. The proof is based on arguments of history-dependent variational inequalities. We also study the dependence of the weak solution with respect to the data and prove a convergence result. |
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Keywords: | viscoelastic material frictional contact history-dependent variational inequality weak solution |
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