Plane waves in nonlocal elastic–plastic materials containing voids

Constitutive relations and dynamical equations are derived for nonlocal elastic–plastic solid materials containing voids. The plastic effect is considered through the dislocation of planes from their original position during the deformation process. Four plane waves with distinct speeds are found to travel in the considered medium of infinite extent comprising of three sets of coupled elastic–plastic waves and a lone transverse wave. Each set of the coupled elastic–plastic waves is found to be influenced by nonlocality, plasticity and voids present in the medium. While the lone transverse wave is found to be influenced by the nonlocality only and remains independent of the presence of plasticity and voids in the medium. One of the sets of coupled elastic–plastic waves disappears in the absence of plasticity from the medium. Numerical computations are performed for a particular model to understand the propagation characteristics of the existed waves. The effects of various parameters are noticed on the propagation characteristics, depicted graphically and explained.