Evaluation of a physical length scale for granular materials

Classical continuum mechanics considers the interaction of microstructural units of the material through stresses and displacements of material points. Therefore, conventional continuum mechanics approaches can not incorporate any intrinsic material length scale. However in reality interaction of grains may include rotations and the corresponding couple stresses as well, and real materials have a number of important length scales (e.g., grains, particles, fibers, etc.). An equation for determining the length scale is proposed. The proposed length scale equations include the effect of plastic deformation (microrotation), the effect of normal stress and contact area. The proposed length scale is implemented into elastic-elastoplastic Cosserat formulation. The effect of length scale on the finite element simulation and yield surface was evaluated by using the proposed length scale equation. The importance of length scale on the constitutive modeling of granular materials is analyzed in numerical simulations.