Deformation Measures for Granular Materials

TL;DR

This paper introduces a micromechanical deformation representation for 2D granular materials, enabling detailed analysis of local deformation and rotation, with applications demonstrated through numerical simulations.

Contribution

It generalizes existing models by applying a consistent, unique assignment of contact displacements to average deformation, and develops data structures for Discrete Element Method simulations.

Findings

Deformation in granular assemblies is highly nonuniform at low strains.

Micro-bands of intense rotation form during deformation.

The method allows detailed resolution of deformation at the particle scale.

Abstract

The paper presents a micromechanical representation of deformation in 2D granular materials. The representation is a generalization of K. Bagi's work and is based upon the void-cell approach of M. Satake. The general representation applies to a material region partitioned into polygonal subregions. This representation possesses a certain consistency that allows for a unique assignment of the contribution that each contact displacement makes to the average deformation of an assembly. The paper addresses construction of the particle graph and appropriate data structures for use with the Discrete Element Method. The approach is applied in a numerical simulation of a two-dimensional assembly of disks. The author presents results of the distributions of deformation and particle-group rotation, with a resolution of about a single particle diameter. Deformation was very nonuniform, even at low strains. Micro-bands, thin linear zones of intense rotation, were also observed.