Numerical models were developed to simulate the propagation of elastic and electromagnetic waves in an arbitrary, dense dispersion of spherical particles. The scattering interactions were modeled with vector multipole fields using pure-orbital vector spherical harmonics, and solved using the full vector form of the boundary conditions. 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 in an iterative fashion to a convergent solution. The addition theorems were rederived in this work using an integral method, and were shown to be numerically equivalent to previously published theorems. Both ordered and disordered collections of up to 5,000 spherical particles were used to demonstrate the ability of the scattering models to predict the spatial and frequency distributions of the transmitted waves. The results of the models show they are qualitatively correct for many particle configurations and material properties, displaying predictable phenomena such as refractive focusing, mode conversion, and photonic band gaps. However, the elastic wave models failed to converge for specific frequency regions, possibly due to resonance effects. Additionally, comparison of the multiple-scattering simulations with those using only single-particle scattering showed the multiple-scattering computations are quantitatively inaccurate. The inaccuracies arise from nonconvergence of the translational addition theorems, introducing errors into the translated fields, which minimize the multiple-scattering contributions and bias the field amplitudes towards single-scattering contributions. The addition theorems are shown to converge very slowly, and to exhibit plateaus in convergence behavior that can lead to false indications of convergence. The theory and algorithms developed for the models are broad-based, and can accommodate a variety of structures, compositions, and wave modes. The generality of the approach also lends itself to the modeling of static fields and currents. Suggestions are presented for improving and implementing the models, including extension to nonspherical particles, efficiency improvements for the algorithms, and specific applications in a variety of fields.

An experimental study is presented here to understand the stress transmission characteristics under different geometrical arrangements of particulates inside a narrow chamber subjected to axial compression loading. The multi-grain systems considered here are face-centred, simple cubic and poly-dispersed structures, as well as inclusions embedded inside seeded, unseeded and cohesive powder bed of Durcal (calcium carbonate). The distribution of the maximum shear stress, direction of the major principal stress and shear stress concentration factor were obtained using photo stress analysis tomography (PSAT). The results show that the maximum shear stress distribution in the simple cubic structure is chain-like and self-repetitive, i.e., a single grain behaviour is representative of the whole system. This is not the case in the case of other granular packing. In the case of the inclusion surrounded by powder media, the maximum shear stress distribution in the inclusion occurs through ring-like structures, which are different from those observed in the structured granular packing. This tendency increases for an increase in the cohesivity of the surrounding particulates. In the granular systems, the direction of the major principal stress is mostly orthogonal to the direction of loading except in some particles in the random granular packing. In the case of inclusion surrounded by Durcal particulates, the directional of the major principal stress acts along the direction of the axial loading except in the ring region where this tends to be oblique to the direction of axial loading. Estimates of the shear stress concentration factor (k) show that, k tends to be independent of the structural arrangement of granular packing at higher load levels. In the case of inclusion surrounded by powder bed, k for the seeded granulated particulate bed is mostly independent of the external load levels. In the case of unseeded particulate (granulated) bed, a fluctuation in k is observed with the loading level. This suggests that the seeded granules could distribute stresses in a stable manner without much change in the nature of shear stress-transmitting fabric of the particulate contacts under external loading. An increase in the cohesion of particulate bed results in more plastic deformation as shown by the differential shear stress concentration factor. The results reported in this study show the usefulness of optical stress analysis to shed some scientific lights on unravelling some of the complexities of particulate systems under different structural arrangements of grains and surrounding conditions of the inclusions in particulate media.