Abstract
We will derive a constitutive relationship
for the stress tensor of an anisotropic rod-like assembly of granular
particles where not only the transverse isotropy (denoted by a unit vector
n, also called the fiber direction) is included, but also the
dependence of the stress tensor T on the density gradient, a
measure of particle distribution, is studied. The granular media is assumed
to behave as a continuum, and the effects of the interstitial fluid are
ignored. No thermodynamical considerations are included, and using
representation theorems, it is shown that in certain limiting cases,
constitutive relations similar to those of the Leslie-Ericksen liquid
crystal type can be obtained. It is also shown that in this granular model,
one can observe the normal stress effects as well as the yield condition, if
proper structures are imposed on the material coefficients.