Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings

Modelling granular materials can help us to understand their behaviour on the microscopic scale, and to obtain macroscopic continuum relations by a micro-macro transition approach. In this paper, the Discrete Element Method (DEM) is used to investigate the influence of the irreversibility at the contact level on the macroscopic behaviour of granular packings in the context of an elasto-plastic cohesive contact model. From the microscopic contact characteristics the effective stiffness parameters are determined at different volume fractions. The conventional way to calculate the stiffness of a packing is to apply compression or shear strain to the entire system and measure the stress response. The results show that the stiffness of the packings increases with the volume fraction as expected. Surprisingly, the samples experience multiple regimes depending on the applied strain and the hysteretic contact model. In the limit of elastic regime at very small strain, all contacts have equal unloading (reversible) stiffness k ₂ . As the strain increases, the contacts transit to the loading stiffness branch and the macroscopic stiffness show a second plateau, where the microstructure of the packing does not change but the contact forces do due to the (irreversible) transition from the unloading to the loading branch and the corresponding reduction in stiffness by k ₁ ∕k ₂ . Only for much larger strain particles start to rearrange and the overall behaviour becomes plastic.