Stability and fluctuations in granular materials during the critical state regime
Résumé
Referring to small strain continuum mechanics, a material is unstable if a spontaneous release in kinetic energy can occur following a small perturbation, consistently to the second-order work Hill's instability criterion. Based on a 2-D discrete element method (DEM), this manuscript investigates the stability of granular assemblies in relation with the elastic energy processes along a biaxial loading. The evolution of relevant stability indexes shows that the strong degree of instability very close to the stress peak is linked with the limited capacity of storing elastic energy, resulting in the bifurcation from unstable state to stable state with the formation of one or multiple shear bands. In the post-bifurcation stage, the significant release in net elastic energy within a dense specimen brings the system in a more stable state where a fluctuation regime develops. On the other hand, the loose specimen undergoes stability fluctuation from the very beginning up to the critical state of biaxial loading. From the perspective of configurational mechanisms, the stability fluctuation stems from loops transformations entailing repeated energy storing and release. Such changes in microstructural topology continuously adjust the mesostructures under external loading to approach a stable bifurcated branch in the form of stability fluctuations.
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