Analysis of a dynamic frictional contact problem for hyperviscoelastic material with non-convex energy density

Mikaël Barboteu (1) , Leszek Gasiński (2) , Piotr Kalita (2)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 UJ - Uniwersytet Jagielloński w Krakowie = Jagiellonian University

Using the time approximation method we obtain the existence of a weak solution for the dynamic contact problem with damping and a non-convex stored elastic energy function. On the contact boundary we assume the normal compliance law and the generalization of the Coulomb friction law which allows for non-monotone dependence of the friction force on the tangential velocity. The existence result is accompanied by two numerical examples, one of them showing lack of uniqueness for the numerical solution.

Mots clés: dynamics; hyperelasticity; viscosity; normal compliance; non-monotone friction; weak formulation; time approximation; existence result; non-uniqueness; numerical simulations

Domaines: Mathématiques [math]

Mikaël Barboteu, Leszek Gasiński, Piotr Kalita. Analysis of a dynamic frictional contact problem for hyperviscoelastic material with non-convex energy density. Mathematics and Mechanics of Solids, 2017, ⟨10.1177/1081286517718604⟩. ⟨hal-01691926⟩