Thermomechanics of dense granular materials: a particle-scale perspective

Abstract

The paper presents a broad thermomechanic framework for the isothermal rate-independent constitutive behavior of dense granular materials. The essential quantities in this framework are directly measurable in discrete element (DEM) simulations: free energy, dissipation, stress, and strain. The paper proposes that energy and dissipation are governed by two sets of internal variables: fabric variables that control the reversible stiffness and structure variables associated with internal sliding. The relevant fabric variables are identified and measured with simulations. Two hypotheses are considered for the structure variables: the macro-scale irreversible strain and an aggregate measure of the micro-scale frictional forces among sliding contacts. Both hypotheses are tested with simulations, which allow direct calculation of the internal variables. The paper then demonstrates the manner in which the measured variables are applied in incremental constitutive models. Among other findings are the following. (1) Dissipation from contact sliding is pervasive and occurs in all directions of incremental loading. (2) Contact motions are not reversed by a reversal of the strain direction, and contacts continue to slide when loading is reversed. (3) The free energy can not be assumed smoothly differentiable; instead, Gâteaux derivatives must be used with irreversible effects. (4) Basic assumptions of elastoplasticity are contravened: no region of purely reversible strain exists, no uniform yield direction exists, no uniform flow direction exists, and irreversible strain is not proportional to the projected total strain. A three-mechanism elastoplasticity model, however, closely fit the DEM results, and methods are demonstrated for quantifying the model. The results emphasize that advanced constitutive models are needed for capturing the general incremental behavior of granular materials.