The impact-contact problem of two nonlinearly elastic bodies

Abstract

The dynamic contact problem of two elastic bodies is considered. The bodies are assumed to be made of nonlinearly elastic compressible materials, and mixed boundary conditions must be satisfied over a timedependent region which is unknown a priori. The method of solution involves an iterative procedure which is continued until the correct solution is determined by the satisfaction of the nonlinear elastodynamic equations of motion in the bodies, the boundary conditions along the contact interface (appropriate to perfectly smooth or perfectly adhesive contact), the relation between the total force between the bodies and rate of change of their momentum, the condition that the normal contact stresses are compressive and that no interpenetration occurs outside the contact region. Results are given exhibiting the effect of the presence of the inertial terms, the change of the curvature of the body, the difference in material properties, the nature of the contact and the effect of the nonlinearity on the response to impact.