New Ways to Represent Interparticle Forces as Effective Stresses in a Macroscopic Continuum

Abstract

This paper presents a simple proof of an initially counterintuitive result that the interparticle effective forces in a particulate aggregate can be meaningfully represented using an infinite number of uniaxial stress tensors. The result is shown to be consistent with previous work in particle mechanics. It does not imply that constitutive behaviors are combinations of uniaxial behaviors. A further level of sophisticated continuum approximation is also identified. Some implications for constitutive modeling are discussed.