Semi-analytical framework for stress–conductivity correlations in periodic granular assemblies under compaction

Abstract

The contact network, defined by a fabric tensor, influences phenomena such as force or heat transfer in a granular assembly. The correlation between fabric, stress, and conductivity has, however, been least explored. Furthermore, a link between these quantities may help to build a benchmark method to assist experiments substantially. The present work bridges the gap between the macroscopic quantities, such as stress and conductivity tensor, using its microscopic connection and the fabric tensor. The study presents a few interesting functional forms and non-dimensional macroscopic quantities that couple conductivity, stress, and fabric. The main feature of these functional forms is that they are independent of friction. These functional forms will provide a good estimate of fabric and conductivity which can be used real-time during the experimental investigations as well.