A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

Abstract

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.

The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions

“…Prior to collapse force chains accumulate stored potential energy and this process continues until the force chains reach their peak load, after which buckling occurs and the force chains experience a loss in load-carrying capacity [14]. Furthermore, Tordesillas & Muthuswamy [15] showed that force chain buckling can be elastic or plastic depending on the state of the contact points. Hence, failure is associated with buckling of the strong force chains and  provides a resistance to buckling.…”

Transition dynamics and magic-number-like behavior of frictional granular clusters

“…Load-carrying capacity and energy dissipation form the two halves of mathematical formulations that relate the deformation to the stress in a dissipative material (i.e., continuum models). To achieve reliable and robust predictions, such models must incorporate the kinematics of those rearrangement events which are chiefly responsible for energy dissipation (i.e., internal variables or plastic strains [20,23,26,36]). Knowledge of which conformational transitions are likely to occur when a force chain buckles and their associated probabilities is an essential and heretofore missing element in continuum models [26,30].…”

“…Unravelling the details of these mesoscopic structures and associated frictional rearrangements, and their impact on bulk mechanical response-particularly on the development of failure-presents a great scientific challenge [7,18,20,21]. Indeed, although granular materials have stimulated intense research activity for decades [5][6][7][8], robust predictions of their mechanical behavior under load remain elusive [12,[22][23][24][25][26]. To date, a crucial missing element that limits prediction and control of dense granular behavior, particularly that of inelastic deformation and failure, is a precise understanding of the interplay between the dynamics of prevalent and * Corresponding author: atordesi@ms.unimelb.edu.au persistent particle rearrangements and the evolution to failure of key functional mesoscopic structures, epitomized by major load-bearing force chains [10,14,18,[26][27][28][29][30][31][32]).…”

“…Indeed, although granular materials have stimulated intense research activity for decades [5][6][7][8], robust predictions of their mechanical behavior under load remain elusive [12,[22][23][24][25][26]. To date, a crucial missing element that limits prediction and control of dense granular behavior, particularly that of inelastic deformation and failure, is a precise understanding of the interplay between the dynamics of prevalent and * Corresponding author: atordesi@ms.unimelb.edu.au persistent particle rearrangements and the evolution to failure of key functional mesoscopic structures, epitomized by major load-bearing force chains [10,14,18,[26][27][28][29][30][31][32]). Knowledge of the dynamical rules governing these essential inelastic rearrangements, especially as they relate to the stability of and energy released from force chains, is crucial for reliable model predictions [11,21].…”

Evolution of the Mesoscopic Parameters and Mechanical Properties of Granular Materials upon Loading

“…All of the above studies focused on characterizing the fabric tensor in assemblies of particles. In addition, Tordesillas and Muthuswamy [23] investigated the evolution of both the fabric and contact force in dense granular materials from the perspective of complex networks.…”