A micromechanically-based constitutive model for frictional deformation of granular materials

Abstract

A micromechanically-based constitutive model is developed for inelastic deformation of frictional granular assemblies. It is assumed that the deformation is produced by relative sliding and rolling of granules, accounting for pressure sensitivity, friction, dilatancy (densi®cation), and, most importantly, the fabric (anisotropy) and its evolution in the course of deformation. Attention is focused on two-dimensional rate-independent cases. The presented theory fully integrates the micromechanics of frictional granular assemblies at the micro-(grains), meso-(large collections of grains associated with sliding planes), and macro-(continuum) scales. The basic hypothesis is that the deformation of frictional granular masses occurs through simple shearing accompanied by dilatation or densi®cation (meso-scale), depending on the microstructure (micro-scale) and the loading conditions (continuum-scale). The microstructure and its evolution are de®ned in terms of the fabric and its evolution. While the elastic deformation of most frictional granular assemblies is rather small relative to their inelastic deformation, it is included in the theory, since it a ects the overall stresses. 7

Constitutive relations for cohesionless frictional granular materials

“…they are suddenly out-of-phase with each other. Hence, the resistance due to the fabric, is suddenly reduced to a minimum value, and continues to decrease during the early stages of unloading, as has been shown experimentally and discussed elsewhere (Balendran and Nemat-Nasser, 1993a;Nemat-Nasser, 2000). We therefore conclude that the shear-deformationhistory dependency can be represented by the extrema of the shear strain during each cycle of deformation.…”

“…This assumption generalizes the usual frictional energy loss which is proportional to the applied pressure and the rate of sliding : , the proportionality coefficient, M f , being the friction coefficient. By setting the rate of frictional loss equal to the rate of plastic work, a relation among parameters relating to dilatancy, fabric, and friction is obtained (Nemat-Nasser, 2000),…”

“…It is assumed that the magnitude of S is given by ¼ psin , where is an effective isotropic friction coefficient. Generalizing the double sliding models (Spencer, 1964(Spencer, , 1982(Spencer, , 1986De Josselin de Jong, 1971;Mehrabadi and Cowin, 1978;Balendran and Nemat-Nasser, 1993a, b), Nemat-Nasser (2000) shows that the inelastic deformation rate tensor, D p , for the two-dimensional case can be represented by…”

Interplay between the inclusions of different sizes and their proximity to the wall boundaries on the nature of their stress distribution within the inclusions inside particulate packing

“…A good level of correlation is reported between them. Such experimental responses were further integrated into the theoretical frameworks for describing the strength characteristics of granular materials [41][42][43]. These studies show that the local fabrics of the particles play a significant role in mobilising the mechanical strength characteristics of particulates at both micro and macro levels.…”

A hypoplastic constitutive model for debris materials

“…Actually, debris materials are normally simplified as solid spherical particle-viscous fluid mixture and treated as a fluid continuum with microstructural effect in the constitutive modeling [10,11]. In most conventional models, constitutive equations for the static and dynamic regimes are formulated and applied separately, such as the models for the solid-like behaviors of granular materials [8,27,41,43] and that for the fluid-like behaviors [1,6,21]. Although some models for granular-fluid flows have taken the stress state of the quasi-static stage into account, the employed theories for the static regime, such as Mohr-Coulomb criterion [34] and extended von Mises yield criterion [32], still fail to determine the changing of pore water pressure from the deformation directly.…”