Propagation of elastic waves through media with thin crack-like inclusions
Wave propagation in elastic homogeneous media containing a random number of thin inclusions is studied. The material of the inclusions is assumed to be elastic or viscoelastic and appreciably softer than the medium surrounding them. Only the principal terms of the expansion of elastic fields in terms of the small parameters of the problem are considered, namely, the ratio of the characteristic linear dimensions of a typical inclusion and the ratio of the characteristic moduli of elasticity of the inclusion and the medium. This makes it possible to replace every inclusion by an equivalent model. The model problem of long-wave scattering by a single thin ellipsoidal inclusion is solved explicitly, and the solution is then used to study a medium containing a random number of thin defects. The effective-field method which takes into account multiple scattering of waves is used to obtain the averaged equation of motion of such a medium (the effective wave operator) in the long-wave approximation. The operator describes the wave propagation in a homogeneous medium with dispersion and attenuation. The velocities of propagation and the attenuation coefficients of various types of elastic waves propagating through materials with randomly oriented inclusions or cracks, and with a system of parallel cracks, are found.
scientific article; zbMATH DE number 3999399