Self-organized criticality in a sheared granular stick-slip system

Muthuswamy

2008

Acta Geotech.

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law-expressed solely in terms of particle scale properties-is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.

Section: Linking Dissipation and Nonaffine Kinematicsmentioning

confidence: 78%

A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

Muthuswamy

2008

Acta Geotech.

“…From Figure 1(b), we observe relatively strong fluctuations in the shear stress after peak. These successive cycles of a decrease (unjamming) followed by an increase (jamming) with strain are characteristic of stick-slip motion identified in other studies [42][43][44][45]. The task is to examine the connections between force chain buckling and dilatation on the mesoscopic scale in periods of unjamming and/or jamming.…”

Section: Identifying Confined Buckled Force Chains or 'Cbfcs'mentioning

confidence: 96%

Stress–dilatancy and force chain evolution

Num Anal Meth Geomechanics

Shi

Tshaikiwsky

2011

SUMMARYThe evolution of internal structure plays a pivotal role in the macroscopic response of granular materials to applied loads. A case in point is the so-called 'stress-dilatancy relation', a cornerstone of Soil Mechanics. Numerous attempts have been made to unravel the connection between stress-dilatancy and the evolution of fabric and contact forces in a deforming granular medium. We re-examine this connection in light of the recent findings on force chain evolution, in particular, that of collective force chain failure by buckling. This study is focussed on two-dimensional deformation of dense granular assemblies. Analysis of individual and collective force chain bucklings is undertaken using data from a discrete element simulation. It is shown that the kinematics of force chain buckling lead to significant levels of local dilatation being developed in the buckling force chain particles and their confining first-ring neighbors. Findings from the simulation are used to guide the development of a lattice model of collective, localized force chain buckling. Consideration of the statics and kinematics of this process yields a new stress-dilatancy relation. The physics of buckling, even at its simplest form, introduces a richness into the stress-dilatancy formulation in a way that preserves the essential aspects of fabric evolution, specifically the buckling mode.

“…Tordesillas et al in the post peak, strain-softening regime. The fluctuations in the shear stress are characteristic of slip-stick motion identified in other studies (Nasuno et al 1998, Albert et al 2001, Dalton and Corcoran et al 2001, Volfson et al 2004. We examined the spatial and temporal distribution of the BFCs.…”

Section: Identifying Confined Buckled Force Chains or ''Cbfcs''mentioning

confidence: 98%

Buckling force chains in dense granular assemblies: physical and numerical experiments

Geomechanics and Geoengineering

Zhang

Behringer

2009

126

119

This paper focuses on the columnar particle structures known as force chains, and their failure via buckling. The local kinematics and frictional dissipation of this failure mechanism are examined quantitatively for dense, cohesionless granular assemblies, under quasistatic and strain-controlled compression. Data are taken from a physical experiment and a discrete element simulation of bidisperse assemblies of circular particles undergoing shear banding. Particular attention is paid to the deformation and dissipation within a class of particle clusters, each composed of a buckled force chain segment and its laterally supporting neighbours. These particle clusters are found to be confined to the shear band. We establish measures of their local micropolar deformation, including nonaffine deformation, and the evolution of these quantities with strain. Temporally and spatially, the kinematics of this class of particles exhibits trends consistent with the particle motions that form the major contributors to deformation on the mesoscopic and macroscopic scales. The predominant mode of contact failure in a force chain undergoing buckling, and in the contacts with and within its laterally supporting neighbours, is frictional rolling. Rolling friction thus serves as one of, if not the main control valve for the energy flow from the force chain to its surrounding medium.