This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, P, and the mean contact number, Z. This relationship applies to the shear stress τ, except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as P, τ and Z are strongly hysteretic functions of the strain, ε. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks.We focus on a path corresponding to pure shear strain, starting from a packing fraction where there is no observable stress. As we strain the system, the detected stresses and mean contact number Z increase, and the system reaches a jammed state for Z's above Z ≃ 3. As we further deform the system, including reversal of the strain, Z tends to remain at or above 3 for much of the time. Throughout, multiple shear cycles, the packing fraction φ remains at a fixed value, φ = 0.758, that is below the observed jamming value for isotropic compression [2]. When the shear strain is reversed, the original force network largely vanishes, and a new strong network forms. This process is strongly hysteretic in the strain, but we find that the stresses can be characterized rather well in terms of the system-averaged contact number, Z.In the remainder of this work, we first describe basic features of the experimental techniques. We then present results from cyclic pure shear experiments, in which we explore the structural and stress changes within each shear cycle and in particular during shear reversals. We then analyze the force network in terms of strong and weak components.

We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively. DOI: 10.1103/PhysRevE.80.060303 PACS number͑s͒: 45.70.Ϫn, 64.60.Ϫi, 83.80.Fg A striking feature of dry granular materials and other athermal systems is that they form force chain networks in response to applied stress, with large forces distributed inhomogeneously into linear chainlike structures ͓1,2͔. A number of experimental studies have visualized and quantified these networks in granular systems using carbon paper ͓3͔ and photoelastic techniques ͓4,5͔. These studies demonstrated that geometrical and mechanical properties of force chain networks are acutely sensitive to preparation procedures, especially near the jamming transition ͓6͔. For example, in isotropically compressed systems, force networks are ramified with only short-ranged spatial correlations of the stress. In contrast, in sheared systems, aligned force chains give rise to longer-ranged stress correlations in the compressive direction.Developing theoretical descriptions for the mechanical properties of granular media is challenging for several important reasons ͓7-10͔: ͑1͒ since tensile stresses are absent in dry granular materials they only remain intact via applied stress, making the limiting zero-stress isostatic state-where the number of degrees of freedom matches the number of constraints ͓11-13͔-problematic; ͑2͒ forces at the microscopic level are indeterminate due to friction and disorder; ͑3͒ granular materials are athermal, so that conventional energy-based statistical approaches are not appropriate; and ͑4͒ near isostaticity we expect fluctuations to be important, both within a single realization of a system and from realization to realization. New methods are needed to bridge the gap between force networks at small length scales and continuum elastoplastic theory at large scales, and to capture the highly sensitive, fluctuating behavior of granular systems near jamming.In this Rapid Communication, we construct a model for stress fluctuations based on grain-scale force and torque balance, positivity of contact forces, and entropy maximization. We then calculate stress correlations and predict differences for systems under isotropic compression versus pure shear. We also perform complementary numerical simulations and experimental studies of jammed granular systems in twodimensions ͑2D͒ subject to isotropic compression and pure shear. The stress correlation functions from theory, simulation, and experiment are in qualitative and in some cases quantitative...

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