Strain Tensor and Deformation for Granular Material

Abstract

A micromechanical analysis is carried out to introduce a tensor measure for the strain of granular media. This strain tensor, being different from that of the conventional definition, includes explicit descriptions for the spin of particles in granular media. A stress‐strain relationship is then derived based on the new definition of strain tensor. Due to the assumption of a linear displacement field, the stress‐strain model is intended for estimating mechanical properties of a packing under conditions of low shear stress levels. The Hertz‐Mindlin theory of nonlinear contact is used in the mathematical model to predict the mechanical behavior of rod assemblies with various packing structures. The theoretical predictions are compared with the measured results obtained from experimental tests. Results of this comparison are used to evaluate the applicability of the stress‐strain model. The laboratory device, test samples, and loading conditions are described and the comparisons between measured and theoretical results are discussed.