Chinese Journal of Theoretical and Applied Mechani ›› 2007, Vol. 23 ›› Issue (2): 223-237.DOI: 10.6052/0459-1879-2007-2-2005-605

• Research paper • Previous Articles     Next Articles

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

Shunying Ji   

  • Received:2005-12-01 Revised:2006-06-14 Online:2007-03-18 Published:2007-03-18

Abstract: Granular materials can be regarded neither as solid media, nor as liquid media, but behave as solid or liquid media under some conditions, and even there is a quasi-solid-liquid phase transition. Granular materials can be modeled with a plastic constitutive model or the kinetic theory of molecular dynamics in the quasi-static or fast flow state, respectively. However, in the quasi-solid-liquid phase transition, the constitutive model is still an open problem. To develop an effective constitutive model for granular materials in the phase transition, the basic dynamic characteristics of granular materials should be determined in details. In this study, a simple shear flow of granular materials is simulated with a 3D discrete element model (DEM) in various concentrations and shear rates, and the phase transition between fast flow and quasi-static flow is obtained. Since the granular materials are normally of various sizes under natural conditions, the particles of granular flow modeled here are in a multi-size state. Based on the simulated results, it is found that the macro-stress is independent of shear rate in the solid phase, and is a linear function of the square of the shear rate in the liquid phase. In the quasi-solid-liquid phase transition, the macro-stress shows a complex correlation with the shear rate. Based on the simulated variables of macro-stress, contact time number, coordination number, and particle number of clusters, etc., the basic characteristics of granular materials in the phase transition are analyzed in details. The effective friction coefficient, net contact time number and coordination number at some medium concentrations can be treated as the phase transition point. Adopting various friction and restitution coefficients, the granular systems still have apparent quasi-solid-liquid phase 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, an exponential constitutive model for multi-size granular materials is developed, and some parameters are determined based on the simulation data. With the physical experimental results measured in a shear cell, the form of this constitutive model, i.e. the relationship between macro-stress and shear rate in different flow states, is validated.

Key words: multi-size granular materials, quasi-solid-fluid phase transition, constitutive equation, coordination number, contact time number