Response to controlled perturbations in frictional granular jamming

Jamming in frictional granular media results in metastable configurations due to stability imparted by frictional contacts against sliding. We experimentally study the frictional energy differene (ΔE) between an unperturbed and a perturbed configuration subject to uni-axial compression under identical conditions in a two-dimensional system comprised of a bidispersed set of disks whose friction we tune through contact roughness d. The homogeneous system-wide acoustic perturbations are independently tuned with amplitude A and frequency f. We find the frictional stress σ released from perturbation follows a stretched exponential form σ = σ₀ exp[-(ΔE/T_eff)^β], where σ₀ is the unperturbed stress, T_eff = (1/2)M (A_RMS f_RMS)², M is total mass of disks in the configuration, and A_RMS and f_RMS are the respective RMS perturbation amplitude and frequency; the stretched exponent β is the only fit parameter. At low T_eff, we obtain a best fit around β ~ 1/3. As T_eff increases and more frictional stress is relieved, the stretched exponent β transitions smoothly and approaches an asymptotic value of β = 1 with an Activated or Arrhenius-like relaxation behavior. Eventually when A_RMS ≥ d, all frictional stresses in the system are relieved and frictionless jamming behavior is recovered.