Granular materials are the second most manipulated material in industry, only after water. They span the wide spectrum ranging from assemblies of non-cohesive particles (e.g. agricultural products in silos and hoppers, sands, etc.) to consolidated solids formed of particulate precursors (e.g. concrete and pharmaceutical tablets). Due to their discrete and heterogeneous nature, variety of microstructural features (e.g. grain and surface morphological properties), variety of grain-pair interaction mechanisms, and loading-induced anisotropic evolution of microstructure, these materials manifest interesting behavior traits. Further, manipulating the microstructural features and the corresponding micromechanical properties of grain-pair interactions can result in metamaterials with unprecedented tailored properties. Developing an understanding of the macroscopic behavior of these materials as well as its connection to the micro-scale phenomena happening at grain-scale is, therefore, essential for analysis of existing materials as well as designing metamaterials.
Our research is aimed at deriving a multiscale modeling methodology which exploits the benefits of discrete models (i.e. explicit representation of microstructure and high levels of detail in the result) and continuum viewpoints (i.e. computational affordability). This holistic approach will be able to accurately, yet efficiently, incorporate micro-scale information into the macroscopic modeling process. This will be done through a multiscale methodology based on a nested handshake of a discrete model, Particle Mechanics Approach (PMA) and a micromechanics-based continuum model, Granular Micromechanics Approach (GMA). PMA derives the material behavior by resolving every contact and will incorporate coupled nonlocal interaction between various contact deformations on each particle. GMA, on the other hand, uses a statistical representation of microstructure by introducing density functions representing the directional distribution of contact properties. By incorporating fluctuations and higher gradients of grain motions, a GMA-based generalized continuum theory, capable of predicting nonclassical phenomena such as wave dispersion, frequency band-gaps, and localization band width will be derived.