Statistical properties of a 2D granular material subjected to cyclic shear

Abstract

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.

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“…[11,13,23,24]. Also the anisotropy of the contact network varies, as related to the opening and closing of contacts, restructuring, and the creation and destruction of force-chains, as confirmed by DEM simulations [15,25]. This is at the origin of the interesting behavior of granular media, but is neglected in many continuum models of particulate matter.…”

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“…In the last years, there has been also an important experimental effort aimed at identifying particle contacts (or forces) which are then used to construct a network [30,31]. However, under experimental conditions it is always difficult to establish with certainty if there is contact between adjacent particles.…”