Development of Micromechanical Models for Particulate Media: The Role of Mesoscale Kinematics and Non-affine Motion in the Transition from Particle to Bulk Mechanical Properties

摘要

Fluctuations in particle kinematics manifest themselves in deforming dense granu- lar assemblies via self-organized pattern formation. In particular, highly correlated structures emerge at multiple length scales spanning the mesodomain. This study is part of an overall effort to quantitatively characterize the evolution of these patterns via measures of non-affine motion at multiple length scales. We present two mea- sures of non-affine motion, viz. global and local. The global measure represents the deviation of particle motion from a material grid moving with respect to the bound- aries; while the local measure corresponds to deviation of particle motion from that dictated by the local strain for a particle. In an attempt to establish the underlying mechanisms of deformation leading up to shear banding and failure, we examined patterns of non-affine motion and correlated trends emerging at these two scales for a densely packed cohesionless assembly under biaxial compression. The following consecutive modes of deformation were identified during the course of the compres- sion test: uncorrelated motion of particles (i.e. random walk diffusion), collective motion of mesoscale particle clusters and microbands, and a single prevailing shear band that splits the assembly into two effectively rigid blocks of particles which can ultimately slide past each other at the point of failure.