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.