[Modélisation des solides cellulaires selon Cosserat]
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.
Révisé le :
Publié le :
Mot clés : milieux continus, homogénéisation, micromécanique, théorie de Cosserat, solides cellulaires, mousses, tissus osseux, milieux continus généralisés
Patrick R. Onck 1
@article{CRMECA_2002__330_11_717_0, author = {Patrick R. Onck}, title = {Cosserat modeling of cellular solids}, journal = {Comptes Rendus. M\'ecanique}, pages = {717--722}, publisher = {Elsevier}, volume = {330}, number = {11}, year = {2002}, doi = {10.1016/S1631-0721(02)01529-2}, language = {en}, }
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/
[1] Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity, J. Mech. Phys. Solids, Volume 49 (2001), pp. 1361-1395
[2] Size effects in ductile cellular solids. Part I: modelling, Int. J. Mech. Sci, Volume 34 (2000), pp. 681-699
[3] Size effects in ductile cellular solids. Part II: experimental results, Int. J. Mech. Sci, Volume 34 (2000), pp. 701-713
[4] Strongly Cosserat elastic lattice and foam materials for enhanced toughness, Cellular Polymers, Volume 12 (1993), p. 17
[5] Cosserat overall modeling of heterogeneous materials, Mech. Res. Comm, Volume 25 (1998), pp. 449-454
[6] Computation of coarse grain structures using a homogeneous equivalent medium, J. Phys. IV, Volume 8 (1998), pp. 197-205
[7] A micromechanically based couple-stress model of an elastic two-phase composite, Int. J. Solids Structures, Volume 38 (2001), pp. 1721-1735
[8] An estimation of overall properties of heterogeneous Cosserat materials, J. Phys. IV, Volume 8 (1998), pp. 111-118
[9] Asymptotic analysis of heterogeneous Cosserat media, Int. J. Solids Structures, Volume 38 (2001), pp. 4585-4608
[10] On certain two-dimensional applications of the couple stress theory, Int. J. Solids Structures, Volume 4 (1968), p. 15
[11] Computational simulation of deformation behavior of 2D-lattice continuum, Int. J. Mech. Sci, Volume 40 (1998), p. 857
[12] Spring network models in elasticity and fracture of composites and polycrystals, Comput. Math. Sci, Volume 7 (1996), pp. 82-93
[13] Analogy between micropolar continuum and grid frameworks under initial stress, Int. J. Solids Structures, Volume 8 (1972), pp. 327-346
[14] Fracture analysis of cellular materials: a strain gradient model, J. Mech. Phys. Solids, Volume 46 (1998), pp. 789-828
[15] Couple-stresses in the theory of elasticity I, Proc. Kon. Nederl. Akad. Wetensch. B, Volume 67 (1964), p. 17
[16] Micromechanical definition of the strain tensor for granular materials, J. Appl. Mech, Volume 118 (1996), pp. 706-711
[17] Cosserat modelling of an elasto-viscoplastic rectangular lattice (Banhart; Fleck; Ashby, eds.), Proceedings of MetFoam 2001, Bremen, 2001
Cité par Sources :
Commentaires - Politique