Propagation of waves in rate-dependent plastic softening rod and beam

The propagation of waves in rods and beams made of rate-dependent softening material is studied in this paper. For rate-dependent materials the governing equation indicates that in the softening state, stress waves may still propagate along the rods arid beams. Transient solutions for semiinfinite rods and beams subjected to impact are obtained, showing that there may exist finite softening regions that travel along the structures. It is found that the length of the softening region and the wave speed depend on the rate sensitivity as well as the softening character of materials.