The dynamic contact with perfect adhesion and frictional slip between a rigid indentor and an elastic half-space

The problem of the dynamic indentation in loading of an elastic half-space by a rigid axisymmetric punch when a finite friction in the contact region is assumed to exist is considered. The problem involves the determination of a timedependent unknown contact area which is composed of an adhesive circular region whose time-dependent radius is a priori unknown, surrounded by a frictional annulus. A numerical procedure based on an iterative process is developed, which is continued until the complete solution is obtained. This solution is determined by the elastodynamic equations of motion, the moving mixed boundary conditions, the requirement that the contact normal stresses are compressive and that no interpenetration occurs outside the contact region. Furthermore, the radius of separation between the locked and slip regions is determined from the requirement that the current shear stresses at the adhesive region cannot exceed the product of the coefficient of friction and the normal stresses, and that within the slip annulus Coulomb law holds. The method is illustrated for a paraboloid indentor and the effect of friction on the elastic field is exhibited.