Modeling of localization in granular materials: Effect of porosity and particle size

The flow stress in the Mohr-Coulomb plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain as a means of modeling the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into a finite element code and used to simulate biaxial shear tests on dry sand. It is shown that the higher order gradient has a significant influence on the material behavior; especially when instabilities such as shear band take place. The gradient term acts as a stabilizer in the post localization regime where material exhibits strain softening. Granular material consists of discrete particles and associated voids. Therefore, a higher order gradient constitutive model must explicitly account for its gradients in terms of the heterogeneous granular microstructure. It is apparent that for the physical problem under consideration the main physical length-scale is the particle size. Furthermore, we argue that there are two main physical mechanisms that seem to control flow, hardening/softening and localization, namely, particle-particle contact (magnitude and heterogeneous directional distribution) and porosity (magnitude and heterogeneous spatial distribution). Therefore, we propose a continuum model that accounts for these mechanisms and associated length scales.