# Comparison of Shear and Compression Jammed Packings of Frictional Disks

## TL;DR

This study compares the structural and stress properties of frictional disk packings generated by compression and shear, revealing similar contact networks but differences in stress anisotropy due to force distributions.

## Contribution

The paper introduces protocols to rejam packings and analyze residual stress differences, highlighting subtle force variations despite similar contact networks.

## Key findings

- Contact number and packing fraction are nearly identical for compression and shear packings.
- Stress anisotropy differs significantly between compression and shear packings.
- Rejammed packings show minimal differences in force distributions compared to original packings.

## Abstract

We compare the structural and mechanical properties of mechanically stable (MS) packings of frictional disks in two spatial dimensions (2D) generated with isotropic compression and simple shear protocols from discrete element modeling (DEM) simulations. We find that the average contact number and packing fraction at jamming onset are similar (with relative deviations $< 0.5\%$) for MS packings generated via compression and shear. In contrast, the average stress anisotropy $\langle {\hat \Sigma}_{xy} \rangle = 0$ for MS packings generated via isotropic compression, whereas $\langle {\hat \Sigma}_{xy} \rangle >0$ for MS packings generated via simple shear. To investigate the difference in the stress state of MS packings, we develop packing-generation protocols to first unjam the MS packings, remove the frictional contacts, and then rejam them. Using these protocols, we are able to obtain rejammed packings with nearly identical particle positions and stress anisotropy distributions compared to the original jammed packings. However, we find that when we directly compare the original jammed packings and rejammed ones, there are finite stress anisotropy deviations $\Delta {\hat \Sigma}_{xy}$. The deviations are smaller than the stress anisotropy fluctuations obtained by enumerating the force solutions within the null space of the contact networks generated via the DEM simulations. These results emphasize that even though the compression and shear jamming protocols generate packings with the same contact networks, there can be residual differences in the normal and tangential forces at each contact, and thus differences in the stress anisotropy.