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

Froiio, F; Tomassetti, G; Vardoulakis, I

dc.contributor.author	Froiio, F	en
dc.contributor.author	Tomassetti, G	en
dc.contributor.author	Vardoulakis, I	en
dc.date.accessioned	2014-03-01T01:24:38Z
dc.date.available	2014-03-01T01:24:38Z
dc.date.issued	2006	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17362
dc.subject	Cosserat continua	en
dc.subject	Granular materials	en
dc.subject	Measure Theory	en
dc.subject.classification	Mechanics	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Grain boundaries	en
dc.subject.other	Measurement theory	en
dc.subject.other	Microscopic examination	en
dc.subject.other	Stress analysis	en
dc.subject.other	Tensors	en
dc.subject.other	Axiomatics	en
dc.subject.other	Cauchy stress tensor	en
dc.subject.other	Contact forces	en
dc.subject.other	Cosserat continuum model	en
dc.subject.other	Granular materials	en
dc.title	Mechanics of granular materials: The discrete and the continuum descriptions juxtaposed	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2006.03.023	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2006.03.023	en
heal.language	English	en
heal.publicationDate	2006	en
heal.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.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/j.ijsolstr.2006.03.023	en
dc.identifier.isi	ISI:000242425800016	en
dc.identifier.volume	43	en
dc.identifier.issue	25-26	en
dc.identifier.spage	7684	en
dc.identifier.epage	7720	en