An experimental investigation of the force network ensemble

We present an experiment in which a horizontal quasi-2D granular system with a fixed neighbor network is cyclically compressed and decompressed over 1000 cycles. We remove basal friction by floating the particles on a thin air cushion, so that particles only interact in-plane. As expected for a granular system, the applied load is not distributed uniformly, but is instead concentrated in force chains which form a network throughout the system. To visualize the structure of these networks, we use particles made from photoelastic material. The experimental setup and a new data-processing pipeline allow us to map out the evolution subject to the cyclic compressions. We characterize several statistical properties of the packing, including the probability density function of the contact force, and compare them with theoretical and numerical predictions from the force network ensemble theory.Comment: accepted for publication in the conference proceedings of Powders and Grains 201

Protocol-Dependence and State Variables in the Force-Moment Ensemble

Stress-based ensembles incorporating temperature-like variables have been proposed as a route to an equation of state for granular materials. To test the efficacy of this approach, we perform experiments on a two-dimensional photoelastic granular system under three loading conditions: uniaxial compression, biaxial compression, and simple shear. From the interparticle forces, we find that the distributions of the normal component of the coarse-grained force-moment tensor are exponential-tailed, while the deviatoric component is Gaussian-distributed. This implies that the correct stress-based statistical mechanics conserves both the force-moment tensor and the Maxwell-Cremona force-tiling area. As such, two variables of state arise: the tensorial angoricity ($\hat{\alpha}$) and a new temperature-like quantity associated with the force-tile area which we name {\it keramicity} ($\kappa$). Each quantity is observed to be inversely proportional to the global confining pressure; however only $\kappa$ exhibits the protocol-independence expected of a state variable, while $\hat{\alpha}$ behaves as a variable of process

Photoelastic force measurements in granular materials

Photoelastic techniques are used to make both qualitative and quantitative measurements of the forces within idealized granular materials. The method is based on placing a birefringent granular material between a pair of polarizing filters, so that each region of the material rotates the polarization of light according to the amount of local of stress. In this review paper, we summarize past work using the technique, describe the optics underlying the technique, and illustrate how it can be used to quantitatively determine the vector contact forces between particles in a 2D granular system. We provide a description of software resources available to perform this task, as well as key techniques and resources for building an experimental apparatus

The influence of interparticle cohesion on rebounding slow impacts on rubble pile asteroids

The ballistic sorting effect has been proposed to be a driver behind the observed size sorting on the rubble pile asteroid Itokawa. This effect depends on the inelasticity of slow collisions with granular materials. The inelasticity of a collision with a granular material, in turn, depends on grain size. Here we argue that determining the inelasticity of such collisions in an asteroid-like environment is a nontrivial task. We show non-monotonic dependency of the coefficient of restitution (COR) on target particle size using experiments in microgravity. Employing numerical simulations, we explain these results with the growing influence of adhesion for smaller-sized particles. We conclude that there exists an optimum impactor to target particle size ratio for ballistic sorting

Enlightening force chains: a review of photoelasticimetry in granular matter

A photoelastic material will reveal its internal stresses when observed through polarizing filters. This eye-catching property has enlightened our understanding of granular materials for over half a century, whether in the service of art, education, or scientific research. In this review article in honor of Robert Behringer, we highlight both his pioneering use of the method in physics research, and its reach into the public sphere through museum exhibits and outreach programs. We aim to provide clear protocols for artists, exhibit-designers, educators, and scientists to use in their own endeavors. It is our hope that this will build awareness about the ubiquitous presence of granular matter in our lives, enlighten its puzzling behavior, and promote conversations about its importance in environmental and industrial contexts. To aid in this endeavor, this paper also serves as a front door to a detailed wiki containing open, community-curated guidance on putting these methods into practice.Comment: 13 page