Work–energy analysis of granular assemblies validates and calibrates a constitutive model

This study presents a rate-independent constitutive model for granular materials which is based on the analysis of discrete element modelling (DEM) results. We examine the elastic and plastic strain rate at any state of shear, and explore how the plastic strain rate and the stress rate are related to some state variables (e.g. stress, void ratio, etc.). The elastic and plastic strain rate are evaluated by assuming that the rate of conservative energy defined in term of elastic strain rate equals the energy rate from work–energy analysis of granular assemblies. The verification of the theoretical work–energy analysis and the acquire of data regarding the mechanical rates at contacts between grains are done through DEM. It is shown that for a representative element volume of granular materials, the external work rate equals the sum of an elastic energy rate and a dissipation rate at contacts. The work rate is either the product of stress and strain rate or the sum of discrete work rate of external forces. Equations regarding the dilatancy, plastic deviatoric strain rate and stress rate are proposed. In the model, a yield surface is not explicitly defined and the deviatoric stress rate is related to not only the elastic deviatoric strain rate, but also a rate of dilatancy. Simulations show that the predictions match both virtual and Toyoura sand satisfactorily in various shear tests within a board range of densities. Additionally, the calibration of parameters is extremely simple. The treatment of cyclic loading condition is also presented.