A Well-Posed Semi-Discretization of Elastodynamic Contact Problems with Friction

It has been shown numerically in previous works that the well-posedness of the spatial semi-discretization plays a crucial role in obtaining stable numerical schemes for elastodynamic frictionless contact problems. The purpose of this paper is thus to introduce a mass redistribution method adapted to elastodynamic contact with Coulomb friction that guarantees the well-posedness of the semi-discrete problem. It is shown that a differentiated treatment has to be applied to the friction condition. Some numerical tests illustrating the gain in stability for the midpoint time integration scheme are presented. They suggest also that, although the differentiated treatment is necessary for the well-posedness, it is not always mandatory from the numerical viewpoint.