Determination of the stress state beneath arbitrary axisymmetric tangential contacts in Hertz-Mindlin approximation based on the superposition of solutions for parabolic contact

Abstract

As an improvement to the recently proposed procedure for the determination of the stress state beneath axisymmetric tangential contacts in Hertz-Mindlin approximation via an appropriate superposition of solutions for the respective flat-punch problem, the determination via the superposition of solutions for parabolic contact is demonstrated. It has two advantages over the flat-punch formulation: the numerical implementation is slightly easier and more stable, due to the absence of stress singularities for the smooth parabolic profile. As a numerical example, the oscillating tangential contact between a rigid indenter with a profile in the form of a power-law (with exponent 4) and an elastic half-space is considered in detail.