GRANULAR MATTER AND THE SCALING LAWS

The granular material is a conglomeration of discrete solids and macroscopic particles characterized by a loss of energy whenever the particles interact. The typical samples in nature include sand grains, soils, debris flows and so on. The corresponding disciplines have been well developed, such as soil mechanics and debris flow dynamics. However, they are mainly phenomenological theories. The granular matter mechanics, which focuses on the fundamental investigations, is relatively new and stays in its infancy stage so far. In this work, the brief history of studies on granular matter was introduced. The remaining open problems, the relations among the granular matter mechanics, soil mechanics and condensed physics are introduced as well. Granular matter is intrinsically multiscale. In-between the particle scale and the system scale, force chains, as the mesoscale structure, stay quasistatic for a period of lifetime. The crosslink of them forms a heterogeneous network, and acts as the key factor that determines mechanical properties such as stability, elasticity and flowability. Especially, an interpretation to the structure of the strong force chain network represents a major work of granular mechanics. In this study, a series of discrete element simulations were conducted on a granular assembly subjected to simple shear. By taking them as examples, the scaling laws for particle scale and force chain scales are explained in details. Finally, a few opinions about strong force chains and the contact connection diagram are proposed.