An anisotropic constitutive relation for the stress tensor of a rod‐like (fibrous‐type) granular material

We will derive a constitutive relationshipfor the stress tensor of an anisotropic rod-like assembly of granularparticles where not only the transverse isotropy (denoted by a unit vectorn, also called the fiber direction) is included, but also thedependence of the stress tensor T on the density gradient, ameasure of particle distribution, is studied. The granular media is assumedto behave as a continuum, and the effects of the interstitial fluid areignored. No thermodynamical considerations are included, and usingrepresentation theorems, it is shown that in certain limiting cases,constitutive relations similar to those of the Leslie-Ericksen liquidcrystal 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, ifproper structures are imposed on the material coefficients