Numerical Methods for Dynamic Contact and Fracture Problems

The present work deals with the numerical solution of dynamic contact and fracture problems. The contact problem is a Signorini problem with or without Coulomb friction. The fracture problem uses a cohesive zone model with a prescribed crack path. These problems are characterized by a non-regular boundary condition and can be formulated with evolutionary variational inequations or di erential inclusions. For the numerical solution, we combine, as usual in solid dynamics, a nite element discretization in space and time-integration schemes. For the contact problem, we begin by comparing the main methods proposed in the literature. We then focus on the so-called modi ed mass method recently introduced by H. Khenous, P. Laborde et Y. Renard, for which we propose a semi-explicit variant. In addition, we prove a convergence result of the space semi-discrete solutions to a continuous solution in the frictionless viscoelastic case. We also analyze the space semi-discrete and fully discrete problems in the friction Coulomb te l-0 05 96 02 9, v er si on 1 26 M ay 2 01 1 case. For the dynamic fracture problem, using a fully explicit scheme is impossible or not robust enough. Therefore, we propose time-integration schemes where the boundary condition is treated in an implicit way. Finally, we present and analyze augmented Lagrangian methods for static fracture problems.