Multiple Scattering Approximation of Anti-plane Elastic Waves in Infinite and Half-Space Domains with Distributed Inclusions

This paper presents an approximation for multiple scattering of elastic waves in the frequency domain by cylindrical inclusions. The problem is reduced to a 2D model by assuming circular inclusions. These inclusions are distributed at randomly selected points in 2D isotropic solids. Infinite and half-space matrices are considered. The inclusions are subjected to an anti-plane (SH) incident wave. The proposed approximation is based on the assumption that the multiple scattering displacement is the summation of the effects of all the possible wave propagation paths. If a wave hits one inclusion, the wave is scattered and part of it scatters to the calculation point. The wave also scatters to the other inclusions and thus repeating the process. This process is repeated a lot of times but the scattered wave becomes smaller as the path length increases and thus becomes negligible up to a certain order. Each of these scattered waves is approximated using the displacements calculated using the boundary element method with farfield approximation for a single scatterer. Using the proposed approximation, the computational time and the memory requirement are considerably reduced as compared to the conventional boundary element method. Numerical results for two aligned inclusions, thirty randomly selected and hundred randomly placed inclusions in both infinite and half-space matrices are shown to verify the accuracy of the proposed approximation.