A robust finite element redistribution approach for elastodynamic contact problems

Farshid Dabaghi (1) , Adrien Petrov (1) , Jérôme Pousin (2) , Yves Renard (1, 2, 3)

1 MMCS - Modélisation mathématique, calcul scientifique
2 ICJ - Institut Camille Jordan
3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

This paper focuses on a one-dimensional elastodynamic contact problem and aims to give some new numerical results. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. An approximation of this evolutionary problem combining the nite element method as well as the mass redistribution method that consists on a redistribution of the body mass such that there is no inertia at the contact node, is introduced. Then two benchmark problems (one being new) with their analytical solutions are presented and some possible discretizations using di erent time{ integration schemes are described. Finally, numerical experiments are reported and analyzed.

Mots clés: energy conservation; variational inequality; mass redistribution method; unilateral contact; Numerical solution

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, Yves Renard. A robust finite element redistribution approach for elastodynamic contact problems. Applied Numerical Mathematics, 2016, 103, pp.48-71. ⟨10.1016/j.apnum.2015.12.004⟩. ⟨hal-00917450v2⟩