A semi-explicit modified mass method for dynamic frictionless contact problems

We propose a semi-explicit numerical method for solving dynamic frictionless contact problems. This method combines a modified mass matrix, a central difference time-integration scheme, and an exact enforcement of the contact condition. At each time step, the displacements of the nodes in the interior of the domain are computed in an explicit way, while the displacements of the nodes at the contact boundary are computed by solving a nonlinear problem. Such a method presents the same stability condition as the central difference scheme without contact and achieves a tight energy behavior.We perform numerical simulations, in 1D and 2D, to illustrate the behavior of the proposed method. In particular, we compare our method to a method combining a central difference scheme and an implicit contact condition.