Iterative simulation of elastic wave scattering in arbitrary dispersions of spherical particles

A numerical modeling approach was developed to simulate the propagation of shear and longitudinal waves in arbitrary, dense dispersions of spherical particles. The scattering interactions were modeled with vector multipole functions and boundary condition solutions for each particle. Multiple scattering was simulated by translating the scattered wave fields from one particle to another with the use of translational addition theorems, summing the multiple-scattering contributions, and recalculating the scattering using an iterative method. The approach can simulate 3D dispersions with a variety of particle sizes, compositions, and volume fractions. To test the model, spectra and wave field images were generated from ordered and disordered microstructures containing up to several thousand particles. The model predicted wave propagation phenomena such as refractive focusing and mode conversion. The iterations converged for many particle configurations, but did not converge or only partially converged for certain conditions, specifically large particle dispersions ( > 100 particles) at short wavelengths ( λ ∼ particle diameter). Incorporating viscoelastic damping into the matrix properties reduced these numerical instabilities. The model is currently constrained by these convergence limitations and by the computation of sufficiently high multipole order for large numbers of particles. The theory and initial results for the model are presented.