Coarse-graining Mean and Displacement of Granular Matter

Abstract

In this paper, we emphasize that the thermodynamic basis of displacement concept is finite equilibrium region and quasi-static process. By considering the dynamic process of a particle system undergoing reversible deformation under external force, the spatial and temporal distributions of mesoscopic mass, mesoscopic mass flow, mesoscopic energy, and mesoscopic stress are calculated using corresponding mesoscopic theory (e.g., Hertz contact mechanics). Their macroscopic correspondence is calculated by means of coarse-grained average, and the resulting macroscopic mass and mass flow are substituted into the equation that defines the displacement, and the displacement is calculated by integration.