The effect of local kinematics on the local and global deformations of granular systems

Despite the prevalent use of continuum mechanics for the modeling of granular materials, the controversy surrounding the relationship between the properties of the discrete medium and those of its equivalent continuum has far from abated. The concept of strain is especially problematic. In a continuum body, the strain represents the deformation of an infinitesimal region about a material point. In a discrete granular assembly, however, deformation is governed by the relative motions of the constituent grains. Herein, we introduce a new microstructural definition for the deformation of a granular material within the framework of Micropolar Continuum Theory. The advantages of the new strain definition over existing formulations are: it accounts for particle rotations, it is relatively straightforward to calculate, and its global average matches the macroscopic strain of the assembly. The new definition leads to a patchwork strain field, the existence of which is linked to the nonaffine strain at the particle scale. A key aspect of this study is the construction of a set of local micropolar strain and curvature measures on the scale of a particle and its first ring of neighbors. We dissect these local continuum quantities and, with the aid of discrete element simulations, examine them for a specimen under biaxial compression. New insights are gained on the contributions of the relative particle motions for specific types of contacts at different stages in the deformation history. Results are discussed in light of past experimental findings on shear banding, as well as Oda's hypothesis on force chain buckling.