A weighted residual relationship for the contact problem with Coulomb friction

Anh Le Van (1) , Huynh Tan Tai Nguyen (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

In this work, a weighted residual relationship is proposed as an extension of the standard virtual work principle to deal with the large deformation contact problem with Coulomb friction. This weak form is a mixed relationship involving the displacements and the multipliers defined on the reference contact surface of the contactor and is shown to be equivalent to the strong form of the initial/boundary value contact problem. The discretization in space by means of the finite element method is carried out on the mixed relationship in a simple way in order to obtain the semi-discrete equation system. The contact tangent stiffness is derived and numerical examples are presented to assess the efficiency of the formulation.

Mots clés: Contact Friction; Weighted residual relationship; Finite element method

Domaines: Mécanique [physics.med-ph]; Matériaux

Anh Le Van, Huynh Tan Tai Nguyen. A weighted residual relationship for the contact problem with Coulomb friction. Computers & Structures, 2009, 87 (23-24), pp.1580-1601. ⟨10.1016/j.compstruc.2009.08.013⟩. ⟨hal-01004969⟩