Wave propagation in elastic–plastic material with voids

Abstract

Constitutive relations and governing equations have been developed for an elastic–plastic material with voids having single slip-plane and direction. The plasticity of the material is considered through the dislocation of slip-plane. The propagation of unidirectional plane waves has been explored in an infinite elastic–plastic material with voids, and it has been found that there exist four basic waves consisting of three coupled elastic–plastic waves and a lone transverse wave. The speeds of propagation of all the coupled elastic–plastic waves are found to be affected by the plasticity and void parameters, in general, while the transverse wave is not affected by the plasticity and void parameters at all and travels with the speed of classical transverse waves. Out of the three coupled elastic–plastic waves, two waves are the counterpart of the waves existing in elastic materials with voids, while the third wave is new and has appeared due to the presence of plasticity in the material. One of the coupled elastic–plastic waves that is least affected by the plasticity faces a critical frequency, below which the wave is a nonpropagating wave. This critical frequency arises due to the presence of voids in the medium. The speed of various waves is computed for a specific model and the results that are obtained are presented graphically. At large frequencies, all the coupled elastic–plastic waves propagate with constant speeds, but at low frequencies, they propagate with speeds less than that of the longitudinal wave of classical elasticity. Several earlier known results have been recovered as special cases from the present formulation.