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

Abstract

A numerical modeling approach was developed to simulate the propagation of shear and longitudinal sound 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 theory and initial results for the model are presented, including an integral derivation for the translational addition theorems. The model can simulate 3D material microstructures with a variety of particle size distributions, compositions, and volume fractions. To test the model, spectra and wave field patterns were generated from both ordered and disordered microstructures containing up to several hundred particles. The model predicts wave propagation phenomena such as refractive focusing, mode conversion, and band gap phenomena. The convergence of the iterations ranges from excellent to fair, and is dependent on the field (longitudinal or shear), particle configuration, and elastic wave frequency. The model is currently limited by the computation of sufficiently high multipole order for the simulation of dense particle dispersions.

Histology-based simulations for the ultrasonic detection of microscopic cancer in vivo

“…8 The method was modified to incorporate scattering from inclusions (nuclei) within the particles (cells). A concentric core-shell structure embedded in a medium represented the cell nucleus, cell cytoplasm, and extracellular matrix, respectively.…”

Three-Dimensional Multiple Scattering of Elastic Waves by Spherical Inclusions

“…The convergence of solutions during iterations is another limiting factor for this method. For example [24] , for longitudinal wave field at 600 kHz and for 600 µm glass beads in polymer with 30% volume fraction, numerical results do not converge after 10 iteration steps so that this method fails at this case.…”

“…Due to the virtual memory requirement in a computer, computation and storage of the matrix for coordinate transformation between coordinate systems of every two scatterers are limiting factors for this method [24] . The convergence of solutions during iterations is another limiting factor for this method.…”

“…For multiple scattering of elastic waves by spherical inclusions in arbitrary arrangement, Doyle [24] in 2006 used an iterative method (based on ordered scattering approach) for calculating wave fields in the elastic system. Calculation is carried out at each order of scattering.…”

Projeto e modelagem de metamateriais acústicos e elásticos por ressonâncias Mie.

“…A metodologia seguida para a construção da matriz T de uma inclusão esférica simples é similar à reportada em [30][31][32], já a matriz T para a inclusão esférica multi-revestida será uma extensão das reportadas em [16,50]. …”