The propagation of longitudinal wave in rate-dependent plastic softening materials

Abstract

Transient longitudinal waves in a strain-softening rod has been investigated. For rate-dependent materials, the governing equations are proved to be hyperbolic, thereby indicating that the stress waves in softening state still propagate along the rod. A transient solution for a semi-infinite rod subjected to an axial impact has been obtained, which shows that there exists a finite softening region in the rod and it travels along the rod. It is indicated that the length of the softening region and the plastic wave speed are pertinent to the rate sensitivity as well as to the softening character of material