Patrulescu, FlaviusSofonea, Mircea2022-09-262022-09-262017-12-05Pǎtrulescu, F., & Sofonea, M. (2017). Analysis of a rate-and-state friction problem with viscoelastic materials. <i>Electronic Journal of Differential Equations, 2017</i>(299), pp. 1-17.1072-6691https://hdl.handle.net/10877/16171We consider a mathematical model which describes the frictional contact between a viscoelastic body and a foundation. The contact is modelled with normal compliance associated to a rate-and-state version of Coulomb's law of dry friction. We start by presenting a description of the friction law, together with some examples used in geophysics. Then we state the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. It is in a form of a differential variational inequality in which the unknowns are the displacement field and the surface state variable. Next, we prove the unique weak solvability of the problem. The proof is based on arguments of history-dependent variational inequalities and nonlinear implicit integral equations in Banach spaces.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalViscoelastic materialFrictional contactNormal complianceRate-and-state frictionDifferential variational inequalityHistory-dependent operatorWeak solutionArticle