(112d) Development of Micromechanical Models for Particulate Media: the Projection Problem in the Transition from Particle to Bulk Mechanical Properties

Micromechanics has the potential to resolve many of the deficiencies of constitutive equations developed for particulate continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to particulate media is the projection scheme that relates the continuum variables to the particle scale variables which are subject to direct observation. Projection schemes based on binary contacts do not fully capture important instabilities because they do not consider mesoscale mechanics related to particle aggregates structures such as force chains commonly seen in granular media. It is noteworthy that while discrete element (DEM) analysis serves as the inspiration for the use of binary contact laws in micromechanical constitutive modelling, DEM has the advantage that the evolution of micromechanical variables in a DEM simulation arises as an emergent behavior rather than imposed as in the micromechanical continuum approach. In this paper, the problem is illustrated by comparison of a micromechanical model to particle data observed in computer simulations using DEM. A second model is derived using an enhanced projection scheme to account for mesoscale mechanics. The second model is shown to display strain-softening behavior related to dilatancy and produce realistic shear bands in finite element simulations of particulate behavior in several benchmark experiments, including the biaxial compression and indentation tests. Importantly, the evolution of microscale variables is correctly replicated.