Micromechanics of shear bands

Abstract

In the past, we have developed a micromechanically-based constitutive model of a 2D, monodisperse granular assembly consisting of circular particles, in which the tangential displacements at particle–particle contacts were limited to microslip only i.e. particles do not slide relative to each other. This constitutive law was later extended, using slightly more advanced contact laws, to include sliding contacts, along with the potential for loss of contacts. Furthermore, through these contact laws, evolution of the distribution of contact modes (non-sliding or microslip contacts, sliding contacts and loss of contacts), contact forces and the density of contact directions, can be determined as the deformation proceeds i.e. deformation-dependent anisotropies. In this paper we apply this latter constitutive model to shear band formation in a bi-axial test. Using an initially isotropic sample, we demonstrate that the constitutive model can reproduce the various anisotropies that have been observed in experiments and simulations. Moreover, the predicted shear band properties (e.g. thickness, inclination, prolonged localisation, void ratio) show even better agreement with experimental observations than previously found using our past models. These results take on particular significance when one considers that, in contrast to the constitutive equations traditionally used for granular materials, the micromechanically-based constitutive model presented here contains a direct link to the physical and measurable properties of particles (e.g. particle–particle friction coefficient, particle stiffness coefficients) and so arguably contains no fitting parameters.