Mechanics of particulate media: A lattice-type approach

Abstract

This research is aimed at understanding the mechanical behavior of particulate/granular media using the power of lattice based techniques. In the lattice type model, a particulate assembly is simulated as a lattice/truss network. Nodes are relocated at contacts between a particle and its neighbors/boundaries and are linked by bars to each other. Each particle is replaced by a lattice within its microstructure and particles interact through load transfer at nodes. Constraints are prescribed at the nodes of the lattice to simulate active, deactivated, and reactivated contacts. An assembly of particles is thus transformed into a lattice/truss and is analyzed using standard methods of structural mechanics under appropriate boundary conditions. When a particulate assembly develops into a mechanism (deformation with zero incremental load), further deformation is simulated through a framework that describes the kinematics of the particles (sliding, rolling, and rotation of particles). This framework is formed by introducing nodes at the particle centroids and linking them with bars. Bars linking particles with a non-sliding contact are assigned large stiffnesses relative to bars linking particles with a sliding contact. Numerical tests are conducted on two dimensional assemblies of disks, arranged as very loose and very dense packings under simple shear loading conditions. The results concord with the results of numerical tests conducted using the discrete element method at low strain levels and with photoelastic experiments up to large shear strain levels. The model is applied to study the effects of initial imperfections caused by particles with low elastic modulus. A dense assembly of disks, with 25% of the particles having an elastic modulus 1/100th of the elastic modulus of the remaining particles, resulted in a decrease of 67% for the shear modulus of the whole assembly. The lattice type model is conceptually simple but has some powerful features that can account for initial particle imperfections, anisotropy, and particle crushing.