Multiple Scattering, Coherent Wave Propagation: Modelling the Propagation of Antiplane Elastic Waves in Multi-Cracked Media

The purpose of this study is to model the propagation of antiplane coherent waves in solids containing randomly and uniformly distributed flat or open cracks. The cracks are randomly-oriented or tilted with respect to the coherent wave front. The crack surface is stress-free or undergoes viscous friction. The complex mechanism of multiple scattering between cracks is taken into account. A first study is concerned with the acoustic response of a damaged layer subjected to a normally incident antiplane wave. The amplitudes of the coherent waves inside and outside the layer are evaluated in closed form. It is shown that the layer behaves macroscopically as a dissipative homogeneous medium with appropriate effective acoustic and mechanical properties. Specifically, the associated effective mass density and shear stiffness are defined. The cases of spatially-varying distributions of cracks and Love waves in a near-surface distribution of cracks are then treated. A last application is concerned with populations of frictional shear cracks of variable widths present in the Earth's crust.