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

Franz Chouly,Yves Renard

doi:10.1186/s40323-018-0124-5

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.

Highlights

Introduction and problem settingExplicit time-marching schemes for the dynamics of deformable solids with impact has already been the subject of an abundant literature
Stability properties of Verlet scheme First, we present different energies associated to the solution to Problem (13), and make explicit their relationships
Concluding remarks In this paper, we studied the application of an explicit Verlet scheme for the approximation of elastodynamic contact problems with Nitsche’s method

Summary

Methods

Mass redistribution method for finite element contact problems in elastodynamics. Contact problems in elasticity: a study of variational inequalities and finite element methods. Time-integration schemes for the finite element dynamic Signorini problem. A Nitsche-based method for unilateral contact problems: numerical analysis. A Nitsche finite element method for dynamic contact: 2. Convergence of a space semi-discrete modified mass method for the dynamic Signorini problem. An explicit energy-momentum conserving time-integration scheme for Hamiltonian dynamics. hal-01661608 (2017). https://hal-enpc.archives-ouvertes.fr/hal-01661608