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.

中文翻译：

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基于弹力接触问题的基于Nitsche的显式Verlet时间积分

本文的目的是从理论上和数值上研究Vernet方案，用于弹性动力学问题的显式时间积分，其接触条件采用Nitsche方法近似。这是论文的延续（Chouly等人，ESAIM Math Model Numer Anal 49（2），481-502，2015； Chouly等人，ESAIM Math Model Numer Anal 49（2），503-528，2015），其中有些隐含提出了多种方案（theta-方案，Newmark和一种新的混合方案），并证明了它们在适当的条件下具有良好的定位性和稳定性。对稳定性进行了理论研究，然后通过数值实验和与现有接触问题离散化的数值比较进行了说明。