We show how rigidity emerges in experiments of sheared two-dimensional frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a critical contact number  z = 2.4±0.1, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a sponge-like morphology. While the pressure within rigid structures always exceeds the pressure outside the rigid structures, they are not identified with the force chains of shear jamming. These findings highlight the need to focus on mechanical stability arising through arch structures and hinges at the mesoscale.

We perform pure shear experiments on a monolayer of N = 826 photoelastic bidisperse disks. The two particle radii are R1 = 5.5 mm and R2 = 7.7 mm and the particles are initially confined to an area of approximately L = 0.5 × 0.5 m. Two of the confining walls are controlled by stepper motors; to impose simple shear, one wall moves in while the other moves out in a series of quasi-static steps. After n steps, the shear is reversed back to the initial state. The floor of the shear cell is a porous frit through which air flows to allow the particles to float on a gentle air cushion, creating a system without basal friction. The particles are made of a photoelastic material (Vishay PhotoStress PSM-4) and illuminated by polarized light with an opposing polarizer on the camera.  Using the Photo-elastic Grain Solver (https://github.com/jekollmer/PEGS) we measure the vector contact forces on all particles.

Detailed information about the data format is found in the included readme.txt file.