ALBERT

Description: In contrast to continuum systems where localization or shear banding arises through a bifurcation in a predefined system of differential equations, shear bands emerge in numerical simulations of deforming granular systems with no prescribed mathematical relations other than simple contact forces between particles. Shear bands emerge from the self‐organization of large numbers of particles with long‐range geometrical interactions playing a dominant role; both translation and rotation of particles are important. Granular media therefore deform more like materials with non‐local constitutive relations than materials where only first‐order interactions are relevant. In this paper we adopt a thermo‐mechanical approach and explore the fluxes of energy in the evolving granular system (that has cohesion as well as friction between the particles) as it is loaded through the unstable localization regime, and track the evolution of energy dissipation. As in continua, the sign of the second‐order work defines the emergence of instability in the system. Initially, these instabilities decay into stable configurations of particles but with continued loading, force chains collapse locally to generate geometrically necessary fractures. These zones then propagate to generate localization zones. When these fractures form a continuous network, the system is at the percolation thresh‐hold for broken bonds. However, long before this stage, the second‐order work fluctuates in bursts weakly correlated with bursts in kinetic energy as damage accumulates. This behaviour suggests that any continuum constitutive description of granular media must be (i) non‐local in an anisotropic manner, (ii) micro‐polar, and (iii) involve damage evolution.