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

Vincent Acary 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : This research report 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-α 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-α scheme. The energy conservation and dissipation properties of the Moreau-Jean is firstly shown. In a second step, the nonsmooth generalized-α scheme is studied by adapting the previous works of Krenk and Høgsberg 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.
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Submitted on : Tuesday, September 30, 2014 - 10:48:41 PM
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Vincent Acary. Energy conservation and dissipation properties of time-integration methods for the nonsmooth elastodynamics with contact. [Research Report] RR-8602, INRIA. 2014, pp.29. ⟨hal-01067691v2⟩

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