μ-GM: A purely micromechanical constitutive model for granular materials

Abstract

A strictly micromechanical framework is proposed for the constitutive modelling of granular materials as a variant to existing micromechanically-enriched continuum models. The theory hinges on the fact that the constitutive behaviour of granular materials can be formally written via an incrementally non-linear expression of stress and strain derived from an exhaustive set of key microvariables that statistically describe contact normals and force networks at the lower scale. The model also incorporates key physics uncovered by micromechanical findings of granular material behaviour such as dissipative and non-dissipative deformational mechanisms, including the existence of a unique surface, named Stable Evolution State as a bounding surface to quasi-static stable evolutionary states that generalizes the well-known critical state in soil mechanics. The proposed model, herein coined as μ-GM, acts as a surrogate for a full-blown discrete element method model in that it includes only three intrinsic material parameters complemented with three calibration ones to reveal most salient microstructural information and their evolution during loading history. As such, it can be readily incorporated into standard finite element simulations of boundary-value problems with computations to the resolution of the microscale. The present model currently formulated in 2D conditions can be readily extended to 3D to explore more complex problems with rotation of principal stresses.