Dynamic friction contact problems for general normal and friction laws
Nonlinear Analysis: Theory, Methods & Applications
Singular perturbation approach to an elastic dry friction problem with non-monotone coefficient
Quarterly of Applied Mathematics
Slip-weakening friction on a periodic system of faults: spectral analysis
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Slip-dependent friction in dynamic elasticity
Nonlinear Analysis: Theory, Methods & Applications
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The dynamic evolution of an elastic medium undergoing frictional slip is considered. The Coulomb law modeling the contact uses a friction coefficient that is a non-monotone function of the slip-rate. This problem is ill-posed, the solution is nonunique and shocks may be created on the contact interface. In the particular case of the one-dimensional shearing of an elastic slab, the (perfect) delay convention can be used to select a unique solution. Different solutions in acceleration and deceleration processes are obtained. To transform the ill-posed problem into a well-posed one and to justify the choice of the perfect delay criterion, a visco-elastic constitutive law with a small viscosity is used here. An existence and uniqueness result is obtained in three dimensions. The assumptions on the functions implied in the contact model are weak enough to include both the normal compliance and the Tresca model. The following conjecture, based on results of numerical simulations, is stated: in the elastic case, the solution chosen by the perfect delay convention is the one obtained from the solutions of the problem with viscosity, when the viscosity tends to zero.