Cosserat modeling of cellular solids

Patrick R. Onck

doi:10.1016/S1631-0721(02)01529-2

Cosserat modeling of cellular solids
[Modélisation des solides cellulaires selon Cosserat]

Patrick R. Onck ¹

¹ University of Groningen, Micromechanics of Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 717-722.

Résumé
Abstract

Les solides cellulaires doivent leurs propriétés mécaniques directement à leur structure microcellulaire. Néanmoins, la longueur caractéristique du matériau est souvent non-négligeable comparée aux dimensions macroscopiques, ce qui limite le domaine de validité des modèles classiques, basés sur une description continue. En revanche, la théorie de Cosserat offre un cadre continu incorporant naturellement une échelle de longueur liée aux gradients de rotation. Dans cette Note nous proposons un procédé d'homogénéisation permettant de dériver, au niveau macroscopique, les équations constitutives de Cosserat, tenant compte de la morphologie de la microstructure concernée ainsi que le comportement du matériau considéré.

Cellular solids inherit their macroscopic mechanical properties directly from the cellular microstructure. However, the characteristic material length scale is often not small compared to macroscopic dimensions, which limits the applicability of classical continuum-type constitutive models. Cosserat theory, however, offers a continuum framework that naturally features a length scale related to rotation gradients. In this paper a homogenization procedure is proposed that enables the derivation of macroscopic Cosserat constitutive equations based on the underlying microstructural morphology and material behavior.

Reçu le : 2002-03-28
Révisé le : 2002-08-20
Publié le : 2002-10-25

DOI : 10.1016/S1631-0721(02)01529-2

Keywords: continuum mechanics, homogenization, micromechanics, Cosserat theory, cellular solids, foams, bone, generalized continua
Mots-clés : milieux continus, homogénéisation, micromécanique, théorie de Cosserat, solides cellulaires, mousses, tissus osseux, milieux continus généralisés

Affiliations des auteurs :

Patrick R. Onck ¹

¹ University of Groningen, Micromechanics of Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands

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     title = {Cosserat modeling of cellular solids},
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Patrick R. Onck. Cosserat modeling of cellular solids. Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 717-722. doi : 10.1016/S1631-0721(02)01529-2. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01529-2/

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