Using dispersion equation for orthotropic media to model antiplane coherent wave propagation in cracked solids

Attention is focused on the propagation of antiplane coherent wave obliquely incident on mutually parallel and randomly distributed cracks. A fundamental question in this study concerns the ability of describing the coherent wave propagation in all directions from the knowledge of the effective material properties along the effective principal directions, only. Its relevance is illustrated by considering two cases of coherent wave propagation: homogeneous and inhomogeneous waves. For both cases, the effective phase slownesses approximated from the dispersion equation specific for orthotropic homogeneous media are compared to reference results obtained from a direct calculation considering waves obliquely incident on cracks. This work reveals that the effective stiffnesses of this dispersion equation have to be dependent on the propagation direction of the incident wave in order to make this equation consistent.