Conservative discretization algorithms for dynamic contact between nonlinear elastic bodies

The paper proposes to compute dynamic contact between nonlinear elastic bodies by means of conservative discretization algorithms. First, the angular momentum and energy conservation, during the dynamic contact between nonlinear elastic bodies without internal dissipation and frictionless are derived, based of Noether's theorem and a variational principle. On this basis we construct the temporal discretization of the contact conditions following the idea proposed by Simo and Tarnow, obtaining an algorithm of second order. The paper considers the Lagrange multipliers method and penalty regularization with the complementarity condition for finite element discretization. This procedure is general and describes the behaviour of nonlinear elastic bodies including the second Piola-Kirchhoff tensor during the dynamic contact. We solve an example concerning an active contact between two plane bodies.