Average antiplane motion in an elastic solid containing a layer of randomly distributed cracks

The propagation of antiplane waves in an elastic solid containing a random distribution of cracks that are parallel to each other, and oriented at an arbitrary angle relative to the direction of the incident wave, is considered. The approach, which is new, is based on the system of integral equations that describes the motion of a solid containing N cracks. When the cracks are randomly distributed inside a rectangular box, the average wave motion at any point in the cracked solid is obtained. Next, the length of the box is increased to infinity. By taking the limit of the preceding result, keeping the crack density constant, the wave motion corresponding to a cracked layer is obtained. In particular, the wave motion reflected by the layer is evaluated in terms of frequency, crack density, layer thickness, and crack orientation. There is also a transmitted wave motion that propagates into the solid on the other side of the layer. Reflection and transmission coefficients are plotted versus frequency, crack density, layer thickness, and crack orientation. Inside the layer, for small values of the crack density and of the layer thickness, it is shown that the attenuation and the speed of the wave motion reduce to those obtained by assuming the existence of a complex-valued wave number