Yielding in the contact zone of bodies interacting by dry friction

Abstract

A model is developed to describe the yield process in the contact zone of an elastic body and a half-space, which interact at local contacts by dry friction. The constitutive relation of the local contacts account for the difference between static and dynamic dry friction. Various processes in the contact zone for lateral external loading of the body are shown to occur by use of the wave equation and the constitutive relation of the contacts. These processes include the yield process in the contact zone, the restoration of equilibrium and rest at the contacts between each additional slip and the prestressing of the body. A closed-form analytical solution is derived for the complete slip of the contact zone by means of Laplace transforms. The solution shows that the slipping body has a velocity at the moment that the last contact yields. The upper bound of this velocity is proportional to the difference between the maximum static and dynamic fractional forces. The model further shows the occurrence of high frequency energy radiation at low frequency body excitation.