A robust finite element redistribution approach for elastodynamic contact problems

This paper deals with a one-dimensional elastodynamic contact problem and aims to highlight some new numerical results. A new proof of existence and uniqueness results is proposed. More precisely, the problem is reformulated as a differential inclusion problem, the existence result follows from some a priori estimates obtained for the regularized problem while the uniqueness result comes from a monotonicity argument. An approximation of this evolutionary problem combining the finite element method as well as the mass redistribution method which consists on a redistribution of the body mass such that there is no inertia at the contact node, is introduced. Then two benchmark problems, one being new with convenient regularity properties, together with their analytical solutions are presented and some possible discretizations using different time-integration schemes are described. Finally, numerical experiments are reported and analyzed.