The tendency of granular materials in rapid shear ow to form non-uniform structures
is well documented in the literature. Through a linear stability analysis of the solution
of continuum equations for rapid shear flow of a uniform granular material, performed
by Savage (1992) and others subsequently, it has been shown that an infinite plane
shearing motion may be unstable in the Lyapunov sense, provided the mean volume
fraction of particles is above a critical value. This instability leads to the formation
of alternating layers of high and low particle concentrations oriented parallel to the
plane of shear. Computer simulations, on the other hand, reveal that non-uniform
structures are possible even when the mean volume fraction of particles is small. In the
present study, we have examined the structure of fully developed layered solutions,
by making use of numerical continuation techniques and bifurcation theory. It is
shown that the continuum equations do predict the existence of layered solutions
of high amplitude even when the uniform state is linearly stable. An analysis of the
effect of bounding walls on the bifurcation structure reveals that the nature of the
wall boundary conditions plays a pivotal role in selecting that branch of non-uniform
solutions which emerges as the primary branch. This demonstrates unequivocally that
the results on the stability of bounded shear flow of granular materials presented
previously by Wang et al. (1996) are, in general, based on erroneous base states.
Discussion: Fully Developed Plastic Shear Flow of Granular Materials
