Micro-macro scale instability in 2D regular granular assemblies

Instability and stress–strain behavior were investigated for 2D regular assemblies of cylindrical particles. Biaxial shear experiments were performed on three sets of assemblies with regular, albeit increasingly defective structures. These experiments revealed unique instability behavior of these assemblies. Continuum models for the assemblies were then constructed using the granular micromechanics approach. In this approach, the constitutive equations governing the behavior of inter-particle contacts are written in local or microscopic level. The behavior of the RVE is then retrieved by using either kinematic constraint or least squares (static constraint) along with the principle of virtual work to equate the work done by microscopic force–displacement conjugates to that of the macroscopic stress and strain tensor conjugates. The ability of the two continuum approaches to describe the measured stress–strain behavior was evaluated. The continuum models and the local constitutive laws were used to perform instability analyses. The onset of instability and orientation of shear band was found to be well predicted by the instability analyses with the continuum models. Further, macro-scale instability was found to correlate with the instability of inter-particle contacts, although with some variations for the two modeling approaches.