A topological view on microscopic structural evolution for granular material under loading and unloading path

Granular materials demonstrate complex mechanical behaviors due to the irreversible rearrangements at particle scale. The irreversible behaviors of granular materials can be observed after unloading the granular assembly. In this study, biaxial tests of dense and loose granular assemblies are conducted using discrete element method (2D DEM). We investigate the multiscale behaviors of granular materials under loading–unloading-reloading path. Both dense and loose granular assemblies show hysteresis loops, but their underlying mechanisms and meso-structural evolutions are different. The hysteretic behavior of the dense sample is relevant to the dynamics of contact force network and the evolution of contact loops. The approximate linearity of stress–strain relation during unloading and reloading stages is attributed to the robustness of strong contact network, while the nonlinearity of stress–strain relation is related to the evolution of contact topology. Specifically, loops of 4-sides within the contact network play an important role by transforming into smaller or larger loops by losing and joining particles during the unloading and reloading path. The loose compactness of granular media results in the unapparent evolution of structures at the mesoscale. Besides, the roles of strong and weak subnetworks are not distinguished. The fewer changes in contact loops may cause unconspicuous nonlinear deformation.