Abstract :
In recent years a discussion could be followed where the pros and cons of the applicability of the Cosserat continuum
model to granular materials were debated [Bardet, J.P., Vardoulakis, I., 2001. The asymmetry of stress in granular media.
Int. J. Solids Struct. 38, 353–367; Kruyt, N.P., 2003. Static and kinematics of discrete Cosserat-type granular materials.
Int. J. Solids Struct. 40, 511–534; Bagi, K., 2003. Discussion on ‘‘The asymmetry of stress in granular media’’. Int. J. Solids
Struct. 40, 1329–1331; Bardet, J.P., Vardoulakis, I. 2003a. Reply to discussion by Dr. Katalin Bagi. Int. J. Solids Struct. 40,
1035; Kuhn, M., 2003. Discussion on ‘‘The asymmetry of stress in granular media’’. Int. J. Solids Struct. 40, 1805–1807;
Bardet, J.P., Vardoulakis, I., 2003b. Reply to Dr. Kuhn’s discussion. Int. J. Solids Struct. 40, 1809; Ehlers, W., Ramm,
E., Diebels, S., D’Addetta, G.A., 2003. From particle ensembles to Cosserat continua: homogenization of contact forces
towards stresses and couple stresses. Int. J. Solids Struct. 40, 6681–6702; Chang, C.S., Kuhn, M.R., 2005. On virtual work
and stress in granular media. Int. J. Solids Struct. 42, 3773–3793]. The authors follow closely this debate and try, with this
paper, to provide a platform where the various viewpoints could find their position. We consider an ensemble of rigid,
arbitrarily shaped grains as a set with structure. We establish a basic mathematical framework which allows to express
the balance laws and the action–reaction laws for the discrete system in a ‘‘global’’ form, through the concepts of ‘‘part’’,
‘‘granular surface’’, ‘‘separately additive function’’ and ‘‘flux’’. The independent variable in the balance laws is then the
arbitrary part of the assembly rather than the single grain. A parallel framework is constructed for Cosserat continua,
by applying the axiomatics established by [Noll, W., 1959. The foundation of classical mechanics in the light of recent
advances in continuum mechanics. In: The axiomatic method, with special reference to Geometry and Physics, North-Holland
Publishing Co., Amsterdam pp. 266–281, Gurtin, M.E., Williams, W.O., 1967. An axiomatic foundation of continuum
thermodynamics. Arch. Rat. Mech. Anal. 26, 83–117, Gurtin, M.E., Martins, L.C., 1976. Cauchy’s theorem in
classical physics. Arch. Rat. Mech. Anal. 60, 305–324]. The comparison between the two realisations suggests the microscopic
interpretation for some features of Cosserat Mechanics, among which the asymmetry of the Cauchy-stress tensor
and the couple-stress.
