Jamming for a 2D granular material

This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, phi. In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable phi which we identify with as phi(c). It is possible to fit Z and P, to power law expressions in phi-phi(c) above phi(c), and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near phi(c). The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below phi(c), where the application of shear strain at constant phi leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, tau. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant phi first leads to an increase of both tau and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only phi and tau, but also P. P, tau, and Z are all hysteretic functions of shear strain for fixed phi. However, we find that both P and tau are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, vertical bar tau vertical bar = mu P.