Mathematical Problems in Engineering
Volume 2005 (2005), Issue 6, Pages 679-702

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

Mehrdad Massoudi

National Energy Technology Laboratory, US Department of Energy, P.O. Box 10940, Pittsburgh 15236, PA, USA

Received 15 October 2004

Copyright © 2005 Mehrdad Massoudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.