# Force networks and jamming in shear deformed sphere packings

## TL;DR

This paper investigates the conditions and structural features leading to shear jamming in sphere packings, demonstrating that isostatic contact networks and rigidity percolation are key factors in both frictionless and frictional systems.

## Contribution

It provides a theoretical framework for understanding shear jamming, validating the isostatic condition at jamming, and linking rigidity percolation to the jamming transition in sphere packings.

## Key findings

- Isostatic contact number Z = D + 1 holds at jamming
- Shear jamming coincides with percolation of over-constrained regions
- Rigidity percolation occurs before shear jamming in 2D systems

## Abstract

The formation of self-organised structures that resist shear deformation have been discussed in the context of shear jamming and thickening[1-3], with frictional forces playing a key role. However, shear induces geometric features necessary for jamming even in frictionless packings[4]. We analyse conditions for jamming in such assemblies by solving force and torque balance conditions for their contact geometry. We demonstrate, and validate with frictional simulations, that the isostatic condition for mean contact number Z = D + 1 (for spatial dimension D = 2, 3) holds at jamming for both finite and infinite friction, above the random loose packing density. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems[5]. We perform rigidity percolation analysis[6,7] for D = 2 and find that rigidity percolation precedes shear jamming, which however coincides with the percolation of over-constrained regions, leading to the identification of an intermediate phase analogous to that observed in covalent glasses[8].