The quasi-solid-liquid phase transition of non-uniform granular materials and their constitutive equation

Granular materials can be regarded neither as solid media, nor as liquid media,but behave as solid or liquid media under some conditions, and eventhere is a quasi-solid-liquid phase transition. Granular materials can bemodeled with a plastic constitutive model or the kinetic theory ofmolecular dynamics in the quasi-static or fast flow state, respectively.However, in the quasi-solid-liquid phase transition, the constitutive modelis still an open problem. To develop an effective constitutive model forgranular materials in the phase transition, the basic dynamiccharacteristics of granular materials should be determined in details.In this study, a simple shear flow of granular materials is simulated witha 3D discrete element model (DEM) in various concentrations and shear rates,and the phase transition between fast flow and quasi-static flow isobtained. Since the granular materials are normally of various sizes undernatural conditions, the particles of granular flow modeled here are in amulti-size state. Based on the simulated results, it is found that themacro-stress is independent of shear rate in the solid phase, and is a linearfunction of the square of the shear rate in the liquid phase. In thequasi-solid-liquid phase transition, the macro-stress shows a complexcorrelation with the shear rate. Based on the simulated variables ofmacro-stress, contact time number, coordination number, and particle numberof clusters, etc., the basic characteristics of granular materials in thephase transition are analyzed in details. The effective frictioncoefficient, net contact time number and coordination number at some medium concentrations can be treated as thephase transition point. Adopting various friction and restitutioncoefficients, the granular systems still have apparent quasi-solid-liquidphase transition, but their transition points are different.Based on the dynamic behaviors of granular materials in different phases,especially from the relationship between macro-stress and shear rate, anexponential constitutive model for multi-size granular materials isdeveloped, and some parameters are determined based on the simulation data.With the physical experimental results measured in a shear cell, the form ofthis constitutive model, i.e. the relationship between macro-stress andshear rate in different flow states, is validated.