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.

Statistical properties of cell stresses in 2D granular solids

Structural characteristics of two-dimensional elliptic granular packs with various aspect ratios and intergranular friction coeffcients were studied using the Discrete Element Method (DEM). Isotropic compaction from random unjammed state leads to a jammed state with polycrystals of orientationally ordered clusters (OOC). The OOCs were identified using a cluster labelling algorithm, based on the relative angle \Delta\theta between the major axes of two contacting particles. The threshold value of \Delta\theta was optimised to give the strongest correlation between OOCs and the force chain network. We found that the resulting OOC size distribution decays algebraically with an exponent of -2, independently of grain aspect ratio and material properties.

Structural characteristics of ordered clusters in packs of ellipses

Poster Session

poster

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

Raphael Blumenfeld

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Presentations

Statistical properties of cell stresses in 2D granular solids

Structural characteristics of ordered clusters in packs of ellipses

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