Why Do Granular Materials Stiffen with Shear Rate? A Test of Novel   Stress-Based Statistics
  Recent experiments exhibit a rate-dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, \dot{\gamma}. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate-dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence that of (\ln (\dot{\gamma}))^{1/2}. 
Robert P. Behringer, Dapeng Bi, Bulbul Chakraborty, Silke Henkes,   Robert R. Hartley