Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

Abstract

We investigate experimentally the mechanical response to shear of a monolayer of bi-disperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10 −3 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilatancy shear-soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition. Introduction. -Understanding the mechanical properties of dense packings of athermal particles, such as grains, foams and emulsions, remains a conceptual and practical challenge. When decreasing the packing fraction φ, these intrinsically out-of-equilibrium systems lose their rigidity at the so-called jamming transition, φ = φ J , when the confining pressure approaches zero and the particles deformations vanish [1][2][3][4]. In the case of frictionless spheres [2,3], the loss of mechanical stability coincides with the onset of isostaticity : the average number of contacts z decreases to its isostatic value, for which the number of geometrical and mechanical equilibrium constraints exactly match the number of degrees of freedom. Approaching the transition, the material becomes more and more fragile [5], and its linear response, dominated by floppy modes [6], exhibits critical scaling [2][3][4]7].

Local rheological measurements in the granular flow around an intruder

“…5(b) displays a similar banana shape with a radial upstream extension of about half the intruder diameter and a similar azimuthal extension. This correlation betweenε andγ is related to the fact that dense granular media are known to dilate upon transient shear [27,28]. Finally the stress fields [Figs.…”

Experimental Evidence of the Gardner Phase in a Granular Glass

“…In this letter we bring the first direct experimental evidences of the Gardner phase, taking advantage of a well controlled granular experiment, which has already proven to successfully probe the vicinity of the jamming transi-tion in a bi-dimensional granular glass former [25][26][27][28][29][30][31]. More precisely, following the protocol suggested for the numerical detection of the Gardner transition [20,24], taking place at φ G , we perform independent compressions of the same glass and show that for large enough compression, the final state differs from one compression to another.…”

Photoelastic force measurements in granular materials

“…In the past decade, many different experimental teams have used photoelastic force visualization to quantify myriad phenomena. For example, it has been possible to reveal the particlescale anisotropy of the contact forces [10], identify interparticle contacts [11], examine particle shape dependence [12], test the validity of statistical ensembles [13], identify dilatancy-softening [14], measure force chain order parameters [15], evaluate the grain-scale stresses caused by growing plant roots [16,17], follow slow dynamics under shear [18][19][20][21], and quantify fast dynamics [22][23][24][25] Because the photoelastic response is known analytically for circles/ellipses, several of these studies have measured the vector contact forces at every interparticle contact within the granular material [26][27][28]. This paper first provides a review of photoelasticity and how it can be used to create high-quality images of stress within granular material ( §II).…”