Journal of Non-Newtonian Fluid Mechanics, 12 (1983) 31-38 31 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands NEW CONSTITUTIVE EQUATIONS FOR THE RAPID FLOW OF GRANULAR MATERIALS--II M. SHAHINPOOR Department of Mechanical and Industrial Engineering, Clarkson College of Technology, Pots- dam, N.Y. 13676 (U.S.A.) (Received February 11, 1982; in revised form March 30, 1982) Summary This paper complements a previous paper, (J. Non-Newtonian Fluid Mech., 9 (1981) 147), which discussed new constitutive equations for rapid collisionally maintained flow of granular materials as a non-Newtonian microfluid in which the gradient of microrotation played an important role as a kinematic variable. In this article we discuss another variation of such constitutive equations; one for which we do not consider the effects of gradients of the mean microrotation of grains. Derived are expressions for the dispersive normal and shear stresses for a plane shear rapid flow of a granular material in the presence of intergranular slip and friction. These expressions reduce to classical results if friction is set equal to zero. A graph of the variation of stresses versus the friction factor is also presented which reveals a kind of choking phenomenon at larger values of btk. 1. Introduction Recently Shahinpoor and Siah [1] discussed a new set of constitutive equation for a rapid shear flow of granular material in which such materials behaved very much like a class of non-Newtonian microfluids. They consid- ered a collision-slip process for a collisionally maintained rapid granular shear flow and obtained the following relationship for the shear and the normal stress, Txy, and Pyy, respectively: = [ ~ai~rk2XD2y°f(X) } Txy ~k+-~) (COSai +/~k sin ai) X[ Fl(~k , ~i)(du/d y ) 2 + F2(/xk, ffi)D(du/d y )(dw/d y ) + F3(#k, ~,)D2(d~/dy)2], (1)