Simulations of multi-states properties of granular materials based on non-linear granular elasticity and the MiDi rheological relation

Abstract

Granular materials exhibit multi-state behaviors, i.e. solid-like or/and liquid-like mechanical states, depending on the magnitudes of solid fraction and shear stress, as often observed in debris flows in mountainous areas of southwestern China. Appropriate constitutive relations describing this multi-state behavior and in-between transitions, and feasible numerical schemes are of great importance for the studies of granular flows and the predictions of such debris flows. In this work, we present a constitutive relation model to cover these multi-state behaviors by dividing the total stress into elastic and kinetic parts. The elastic stress is deduced from a non-linear elastic energy model we proposed for granular solid recently, the elastic stability criteria, which are based on the ratio of elastic strain invariants, are obtained according to the stability conditions of thermodynamic equilibrium. On the other hand, the kinetic stress is described by using the MiDi rheological relation. Large deformation problems are inviolably encountered in multi-state behaviors of granular materials. In this work, the Material Point Method (MPM) is further developed and simulations are carried out in three cases, namely a steady granular flow, granular pile collapse, and biaxial compression. Results of these three simulations agree well with previously published results. This indicates that both the constitutive model and the MPM method we developed in this study works well for granular materials in multi-states as well as during state transitions. Furthermore, we discuss the finding of a decrease in the effective friction coefficient near the jamming state in granular pile collapse, and also the results reported in recent publications.