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. © 2006 Elsevier Ltd. All rights reserved.

Froiio, F., Tomassetti, G., Vardoulakis, I. (2006). Mechanics of granular materials: the discrete and the continuum descriptions juxtaposed, 43(25-26), 7684-7720 [10.1016/j.ijsolstr.2006.03.023].

Mechanics of granular materials: the discrete and the continuum descriptions juxtaposed

TOMASSETTI, GIUSEPPE;
2006-01-01

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. © 2006 Elsevier Ltd. All rights reserved.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
Con Impact Factor ISI
Cosserat continua; granular materials; measure theory
Froiio, F., Tomassetti, G., Vardoulakis, I. (2006). Mechanics of granular materials: the discrete and the continuum descriptions juxtaposed, 43(25-26), 7684-7720 [10.1016/j.ijsolstr.2006.03.023].
Froiio, F; Tomassetti, G; Vardoulakis, I
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31293
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 27
social impact