Energy conservation and dissipation properties of time-integration methods for nonsmooth elastodynamics with contact

This article is devoted to the study of the conservation and the dissipation properties of the mechanical energy of several time-integration methods dedicated to the elasto-dynamics with unilateral contact. Given that the direct application of the standard schemes as the Newmark schemes or the generalized-alpha schemes leads to energy blow-up, we study two schemes dedicated to the time-integration of nonsmooth systems with contact: the Moreau-Jean scheme and the nonsmooth generalized-alpha scheme. The energy conservation and dissipation properties of the Moreau-Jean is firstly shown. In a second step, the nonsmooth generalized-alpha scheme is studied by adapting the previous works of Krenk and Hogsberg in the context of unilateral contact. Finally, the known properties of the Newmark and the Hilber-Hughes-Taylor (HHT) scheme in the unconstrained case are extended without any further assumptions to the case with contact. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim