Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

Patrick Ballard (1)

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

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.

Mots clés: elasticity; contact; friction; singularity; variational inequality; uniqueness 2010 MSC: 74B05; 74M10; 74M15

Domaines: Mécanique des solides [physics.class-ph]

Patrick Ballard. Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities. Journal of the Mechanics and Physics of Solids, 2016, 97, pp.225-259. ⟨10.1016/j.jmps.2016.03.021⟩. ⟨hal-02326962⟩