Oblique coherent waves inside and outside a randomly cracked elastic solid

Abstract

Propagation of antiplane waves in an elastic solid that contains a cracked slab region is investigated. The cracks have a uniform probability density in the slab region, are parallel to the boundaries of the slab, and the solid is uncracked on either side of the slab. When an antiplane wave is obliquely incident on the cracks, it is shown that the average (coherent) motion in the solid is governed by a pair of integral equations. This result is obtained by taking an average of the exact system of equations for N nonintersecting cracks and by letting N tend to infinity keeping the crack density constant. Then, it is assumed that the average exciting stress near a fixed crack is equal to the average coherent stress, and it is shown that the pair of integral equations yields simple analytical formulas for the complex-valued wave number and the refracted waves inside the slab as well as for the wave amplitudes outside the slab. These quantities depend on incident angle, crack density, frequency, and slab thickness. Numerical results, which are valid for small values of the crack density, are presented as functions of frequency and incident angle.