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Path-dependent analysis of elastic sphere contact subjected to tangential loading with varying directions

The Cattaneo–Mindlin solutions of contact between elastic spheres and their recent extensions do not consider the sequential application of arbitrarily directed shear forces in the contact tangential plane. For this loading condition, the contact tractions simultaneously undergo loading and unloading. This article presents a path-dependent analysis wherein we use superposition at each loading step to obtain the contact tangential traction, and, subsequently the tangential displacement and compliance. The methodology is illustrated by example calculation of contact shear force–displacement relationship, which shows the formation of hysteretic loop and the noncoaxiality of the shear forces and displacements.