Numerical treatment of contact and friction : the contact dynamics method

Jean Jacques Moreau (1) , Michel Jean (2)

1 LMGC - Laboratoire de Mécanique et Génie Civil
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

Difficulties occur in the numerical treatment of mechanical systems when the unilateral constraints of mutual impenetrability of members are taken into account. At every time-step, algorithms have to be ready to handle the possible break.ing of some contacts or, on the contrary, their sudden introduction by collisions. Furthermore, the modeling of dry friction, generally present in the case of contact, rests on mathematically irregular relationships. It is shown in this paper how the numerical approach named 'Contact Dynamics' allows one to calculate evolutions in dynamic or quasi­ static regimes and also to analyze the possible equilibria. This method faces the essential nonsmoothness of the concerned problems without ressorting to the regularizing approximations applied by other commonly used techniques. It rests on time-discre­ tization schemes of the implicit type, allowing for coarser time steps, at the price of applying nonsmooth iteration procedures.

Domaines: Mécanique [physics.med-ph]

Jean Jacques Moreau, Michel Jean. Numerical treatment of contact and friction : the contact dynamics method. Engineering Systems Design and Analysis Conference, 1996, New York, United States. pp.201 - 208. ⟨hal-01825208⟩