Numerical tests of constitutive laws for dense granular flows

We numerically and theoretically study the macroscopic properties of dense, sheared granular materials. In this process we first consider an invariance in Newton's equations, explain how it leads to Bagnold's scaling, and discuss how it relates to the dynamics of granular temperature. Next we implement numerical simulations of granular materials in two different geometries--simple shear and flow down an incline--and show that measurements can be extrapolated from one geometry to the other. Then we observe nonaffine rearrangements of clusters of grains in response to shear strain and show that fundamental observations, which served as a basis for the shear transformation zone (STZ) theory of amorphous solids [M. L. Falk and J. S. Langer, Phys. Rev. E. 57, 7192 (1998); M.R.S. Bull 25, 40 (2000)], can be reproduced in granular materials. Finally we present constitutive equations for granular materials as proposed by Lemaître [Phys. Rev. Lett. 89, 064303 (2002)], based on the dynamics of granular temperature and STZ theory, and show that they match remarkably well with our numerical data from both geometries.