非均匀颗粒材料的类固-液相变行为及本构方程

THE QUASI-SOLID-LIQUID PHASE TRANSITION OF NON-UNIFORM GRANULAR MATERIALS AND THEIR CONSTITUTIVE EQUATION

以非均匀颗粒介质为研究对象,采用三维离散元方法对其在不同密集度和剪切速率下的动力过程进行了数值模拟,分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变过程及其行为特点．通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、配位数、团聚颗粒数量、有效摩擦系数等参量的计算,更加全面地描述了非均匀颗粒材料在类固-液相变过程中的基本特征．基于以上数值计算结果,建立了一个适用于颗粒材料类固态、类液态以及其相变过程的本构方程,并通过剪切室实验结果验证了它的合理性．

Granular materials can be regarded neither as solid media, nor as liquid media, but behave as solid or hquid media under some conditions, and even there is a quasi-solid-hquid 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, how to build 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 macrostress 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-hquid 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.