Abstract

We introduce a mathematical formalism towards the construction of a continuum-field theory for particulate fluids and solids. We briefly outline a research program aimed at unifying the fundamentals of the coarse-graining theory and the numerical method of Smoothed Particle Hydrodynamics (SPH). We show that the coarse-graining functions must satisfy well defined mathematical properties that comply with those of the SPH kernel integral representation of continuous fields. Given the appropriate dynamics for the macroscopic response, the present formalism is able to describe both the solid and fluid-like behaviour of granular materials.