Fabric response to strain probing in granular materials: Two-dimensional, isotropic systems

Abstract

The stress-deformation behaviour of granular media is known to be directly linked to details of the underlying microstructure of contacts, or fabric. The notion of contact fabric and its role in defining stress and strain motivate the present study to explore the evolution of fabric in response to small strain probes applied to initially isotropic granular assemblies of varying void ratios and coordination numbers. Two-dimensional Discrete Element Method simulations demonstrate that the fabric response strongly depends on the strain probe direction, despite the stress response being “pseudo-elastic” and incrementally linear. This direction dependence leads to a so-called incrementally nonlinear property of fabric changes in the small deformation regime, a constitutive characteristic that can serve as a precursor signalling the more intricate, elasto-plastic behaviour of anisotropic granular materials. The present study provides a systematic analysis based on a representation theorem for two-dimensional isotropic functions to characterize fabric changes during strain probing. Contact reorientation is found to be negligible vis-à-vis contact gains and losses which are prevalent in compressive and extension strain probes, respectively. In the end, it is the subtle evolution of gained and lost contacts in various strain probes that helps us elucidate the nature of important fabric changes in the pseudo-elastic regime of granular media.