We are interested in the numerical solution of contact problem in elastodynamics. We present the strong formulation of problem and give the finite element discretization [
]. We prove that the last formulation is not a well posed problem. In order to overcome this difficulty, we propose then an original method based on a redistributed mass matrix. This new mass matrix is assembled conserving the total mass, the gravity center and the momentum inertia.
The discrete elastodynamic contact problem expressed with the redistributed mass matrix is well posed, is energy conserving and has a Lipschitz continuous solution[
Finally, some numerical results are presented to coroborate the theoritical results. Simulations are done with and without the redistributed mass matrix for a Newmark scheme. We remark that the behaviour of the energy and the normal stress are improved using this new method. The energy is quasi-conserved and will be strictly conserved when time parameter goes to zero [