Explicit Verlet time–integration for a Nitsche–based approximation of elastodynamic contact problems

Abstract : The aim of the present paper is to study theoretically and numerically the Verlet scheme for the explicit time-integration of elastodynamic problems with a contact condition approximated by Nitsche’s method. This is a continuation of papers (Chouly et al. ESAIM Math Model Numer Anal 49(2), 481–502, 2015; Chouly et al. ESAIM Math Model Numer Anal 49(2), 503–528, 2015) where some implicit schemes (theta-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed and stable under appropriate conditions. A theoretical study of stability is carried out and then illustrated with both numerical experiments and numerical comparison to other existing discretizations of contact problems.
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Franz Chouly, Yves Renard. Explicit Verlet time–integration for a Nitsche–based approximation of elastodynamic contact problems. Advanced Modeling and Simulation in Engineering Sciences, SpringerOpen, 2018, 5 (31), ⟨10.1186/s40323-018-0124-5⟩. ⟨hal-01814774⟩

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