A Study of Transient Dynamics with Frictional Contact: Oblique Elastic Impact of Spheres

Oblique elastic impact of spheres and the related case for cylinders have been studied cases for many years in simulations of systems with loose supports, such as heat exchanger tube-support interaction, as well as granular flows and robotic task modeling. The problem is a relative simple one in the class of transient frictional contact problems in that the stresses away from the contact zone are typically neglected. The available continuum model solutions from literature show some very interesting features. For near normal angles of incidence, these solutions combine a Hertzian contact stress solution in the normal direction with a partial-slip shear stress distribution in the tangential direction, in which a central portion of the contact zone is sticking while the coincident points of the outer annulus slide relative to one another. Both stress distributions change rapidly over the impact duration. The partial-slip shear stress distribution is caused by the simultaneous inclusion of tangential compliance and friction effects, and gives rise to tangential force reversal prior to the loss of contact. Initial investigations using the penalty contact formulation in Abaqus/ExplicitTM v. 6.7 show some very interesting results. Both the normal and shear stress results show smooth distributions, however the shear stress distributions show an unexpected antisymmetry. Nevertheless, the Abaqus/ExplicitTM solution is able to capture the essential features of tangential force oscillation predicted by continuum models.