title: Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space.
abstract: Solids are distinguished from fluids by their ability to resist shear. In equilibrium systems, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern that is persistent, which in turn results from minimizing the free energy. In this work, we focus on a class of systems where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled by the constraints of mechanical equilibrium. We argue that these constraints can lead to a persistent pattern in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this persistent pattern. We investigate the structure and behavior of patterns both in real space and the dual space as the system evolves through the rigidity transition for a range of packing fractions and in two different shear protocols. We show that, in the protocol that creates homogeneous jammed states without shear bands, measures of shear jamming do not depend on strain and packing fraction independently but obey a scaling form with a packing-fraction-dependent characteristic strain that goes to zero at the isotropic jamming point ϕ_{J}. We demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which provides a quantitative measure of the rigidity of shear-jammed states.
authors.affiliation: Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
authors.forename: Sumantra
authors.initials: S
authors.lastname: Sarkar
authors.affiliation: Department of Physics, Syracuse University, Syracuse, New York 13224, USA.|Center for Studies in Physics and Biology, Rockefeller University, New York, New York 10065, USA.
authors.forename: Dapeng
authors.initials: D
authors.lastname: Bi
authors.affiliation: Institute of Natural Sciences and Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Jie
authors.initials: J
authors.lastname: Zhang
authors.affiliation: Department of Physics, Duke University, Durham, North Carolina, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Ren
authors.affiliation: Department of Physics, Duke University, Durham, North Carolina, USA.
authors.forename: R P
authors.initials: RP
authors.lastname: Behringer
authors.affiliation: Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
authors.forename: Bulbul
authors.initials: B
authors.lastname: Chakraborty