The multiple scattering effect of elastic waves propagation in an inhomogeneous medium

Unraveling the elastic wave propagating in an inhomogeneous medium is critical from both scientific and engineering viewpoints. Here, we propose and validate a double defects model based on unified mechanics framework to study the multiple scattering effect induced by the interaction between elastic waves and defects. The governing equations describing the dispersion and attenuation in frequency space are derived. In order to describe the multiple scattering effect, the Green's function method is employed together with the discrete boundary element method to establish the relation of macroscopic defect density and microscopic defect structure. The results show that the multiple scattering effect originates from the interaction between adjacent defects, and the limit of the multiple scattering (strong interaction) is approximately 6 times the characteristic length of the defect, namely the affected area of a single defect. Due to the stronger interaction, wave velocity decays more seriously for higher defects density than those in the lower density, and there exists no strong coupling between multi-scattering effect and multi-scale effect. The present work provides an efficient way to understand the multi-scattering effect of elastic waves in an inhomogeneous medium.