On the Energy-momentum Conserving Integration of Large Deformation Contact Problems

Dynamic contact problems in elasticity are dealt with in the framework of nonlinear finite element methods. To this end, the mortar method is applied to take into account the constraint of impenetrability. A new energy-momentum conserving time-stepping scheme for the mortar contact formulation is presented. The proposed method relies on a reparametrization of the contact constraints in terms of specific invariants. In this way, the symmetry properties of the underlying finite-dimensional mechanical system can be naturally accounted for by exploiting Cauchy’s representation theorem. For the time discretization of the contact forces emanating from the mortar formulation the notion of a discrete gradient is applied.