A class of implicit variational inequalities and applications to frictional contact

Anca Capatina , Marius Cocou (1) , Michel Raous (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper deals with the mathematical and numerical analysis of a class of abstract implicit evolution variational inequalities. The results obtained here can be applied to a large variety of quasistatic contact problems in linear elasticity, including unilateral contact or normal compliance conditions with friction. In particular, a quasistatic unilateral contact problem with nonlocal friction is considered. An algorithm is derived and some numerical examples are presented.

Mots clés: Mathematics Subject Classification (2000). 35K85; 49J40; 65N12; 65N30 Evolution problems; implicit variational inequalities; quasistatic frictional contact

Mots clés: evolution problems; implicit variational inequalities; quasistatic frictional contact

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Anca Capatina, Marius Cocou, Michel Raous. A class of implicit variational inequalities and applications to frictional contact. Mathematical Methods in the Applied Sciences, 2009, 32 (14), pp.1804-1827. ⟨10.1002/mma.1112⟩. ⟨hal-00461930⟩