LAUSR

Abstract Granular media, a macroscopic amorphous matter composed of mesoscopic discrete particles, exhibits different behaviour characteristics (e.g., solid-, liquid-, and gas-like phases) depending on the volume fraction and loading conditions. Therefore, it poses a significant challenge to three-phase modelling and analysis. In this study, a description of multiple phases in granular media is realised by establishing the transition criteria and parameter conversion relations between different phases, using the already established theories of the elastic-plastic constitutive relation in solid mechanics, the viscoplastic constitutive relation in rheology, and the kinetic theory of granular flow. The new model realises the coexistence of different phases and the conversions therebetween. Smoothed discrete particle hydrodynamics are introduced to discretise the new theoretical model, and the correspondence between the smoothed and actual particles for different phases and discrete formulas under different models are described in detail. Two typical cases are used for numerical tests: the collapse of one side of a three-dimensional granular column and the collapse and flow of a granular column on an inclined surface. The calculated morphology of granular flow, distributions of velocity vectors, scaling law of spreading range under different height-width ratios, and the transient characteristics of particle spreading all accord well with the experimental results. Furthermore, quasi-static, slow, fast, and other phases of particle motions are well captured. Thus, we verify the feasibility of the new model and method for the multiple-phase simulation of granular media.