A microscopic theory for discontinuous shear thickening of frictional granular materials
1 Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
2 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
Published online: 30 June 2017
We extend a recent theory for the rheology of frictionless granular materials  to the case of frictional disks in two dimensions. Employing a frictional contact model for molecular dynamics simulations, we derive difference equations of the shear stress, the granular temperature, and the spin temperature from the generalized Green-Kubo formula, where all the terms are given by microscopic expressions. The numerical solutions of the difference equations not only describe the flow curve, but also reproduce the hysteresis of shear stress, which can be the signature of discontinuous shear thickening of frictional disks.
© The Authors, published by EDP Sciences, 2017
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