Impact of a Nonlinear Viscoplastic Rod on a Rigid Wall

Barenblatt and Ishlinskii [5] considered the impact of a viscoplastic rod on a rigid wall in which the relation between stress and strain rate is linear. In this paper, their analysis is generalized to a power-law relation between stress and strain rate so that their results may be reduced as a special case. Some strikingly different behaviors are observed between linear viscoplastic materials and nonlinear viscoplastic materials. Comparisons are also made between the viscoplastic solution obtained here with the rate-independent, rigid-plastic solution by Lee and Tapper [2]. It is shown that the curves which represent the residual strains versus the axial length along the rod are concave upward for all viscoplastic rods. For the rate-independent, rigid-plastic rods, on the other hand, they are concave downward.