Experimental observations of marginal criticality in granular materials

Abstract

Two drastically different theories predict the marginal criticality of jamming. The full replica symmetry breaking (fullRSB) theory [1-4] predicts the power-law distributions of weak contact forces and small inter-particle gaps in infinite-dimensional hard-sphere glass, with two nontrivial exponents ${\theta }_f=\mathrm{0.42311...}$ and $\gamma =\mathrm{0.41269...}$, respectively. While the marginal mechanical stability (MMS) analysis [5-8] predicts that the isostatic random packings of hard frictionless spheres under external stress are marginally stable and provides inequality relationships for the exponents of the weak-force and inter-particle-gap distributions. Here we measure precisely contact forces and particle positions in isotropic jammed bidisperse photoelastic disks and find the clear power-law distributions of weak forces and small inter-particle gaps, with both exponents ${\theta }_f=0.44(2)$ and $\gamma =0.43(3)$ in an excellent agreement with the fullRSB theory. As the jammed packing subject to area-conserved cyclic pure shear approaches the yielding point, the two exponents change substantially from those of the isotropic case but they still satisfy the scaling relationship provided by the MMS argument. Our results provide strong experimental evidences for the robustness of the infinite-dimensional theory and the MMS analysis in real-world amorphous materials.

arXiv comment7 pages, 3 figures

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• A review on shear jamming
• Non-linear elasticity, yielding and entropy in amorphous solids
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Shear hardening in frictionless amorphous solids near the jamming transition
• Dynamic Gardner crossover in a simple structural glass
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• Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations
• Topological signatures of collective dynamics and turbulent-like energy cascades in apolar active granular
• Particle-scale origin of quadrupolar non-affine displacement fields in granular solids
• The geometry of jamming algorithms in the random Lorentz gas