Statistical properties of cell stresses in 2D granular solids

¹ Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
² Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

^* Corresponding author: tmatsu@kz.tsukuba.ac.jp

Published online: 7 June 2021

Abstract

We investigate numerically the statistics of the stresses, defined for cells - the irreducible loops surrounded by particles in contact - in two-dimensional granular solids and the relation between these cell stresses and cell structures. We prepared a number of mechanically stable granular assemblies at various packing fractions and mean coordination numbers, and measured the stress statistics on each cell. We find the following. (1) The mean cell stress agrees with the bulk external pressure; (2) the probability density function of the normalised cell stress ratio collapses into a master curve; (3) the mean stress ratio increases with increasing intergranular friction; (4) the mean stress ratio per cell order decreases with increasing cell order because of their reduced stability; (5) the maximum cell stress direction correlates well with the cell’s long axis. These results are strong evidence that the cell structure and the stress field self-organise together and reveal the co-evolving correlations between the two.