[Méthode du « second ordre » pour les composites non linéaires et applications aux matériaux isotropes]
On utilise la méthode d'homogénéisation non linéaire proposée par Ponte Castañeda [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737–757], dite du « second ordre », pour générer des estimations pour le comportement effectif et les premiers moments des champs locaux dans des composites non-linéaires. Des expressions analytiques simples sont données non seulement pour les potentiels effectifs mais également pour la relation contrainte-déformation macroscopique, aussi bien que pour les moyennes par phase des champs de contrainte et de déformation. Des estimations du type de Hashin–Shtrikman sont données pour des composites biphasés, isotropes avec des phases suivant une loi puissance, et sont comparées aux résultats exacts disponibles pour les matériaux laminés. L'accord s'avère bon pour toutes les valeurs de la non-linéarité et de concentration d'inclusion considérées.
New prescriptions are proposed for the ‘reference’ fields in the context of the ‘second-order’ nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737–757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, ‘second-order’ estimates of the Hashin–Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered.
Accepté le :
Publié le :
Mot clés : Mécanique des solides numérique, Homogénéisation, Comportement non linéaire, Plasticité parfaite
@article{CRMECA_2006__334_10_575_0,
author = {Mart{\'\i}n I. Idiart and Kostas Danas and Pedro Ponte Casta\~neda},
title = {Second-order theory for nonlinear composites and application to isotropic constituents},
journal = {Comptes Rendus. M\'ecanique},
pages = {575--581},
publisher = {Elsevier},
volume = {334},
number = {10},
year = {2006},
doi = {10.1016/j.crme.2006.06.006},
language = {en},
}
TY - JOUR AU - Martín I. Idiart AU - Kostas Danas AU - Pedro Ponte Castañeda TI - Second-order theory for nonlinear composites and application to isotropic constituents JO - Comptes Rendus. Mécanique PY - 2006 SP - 575 EP - 581 VL - 334 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2006.06.006 LA - en ID - CRMECA_2006__334_10_575_0 ER -
%0 Journal Article %A Martín I. Idiart %A Kostas Danas %A Pedro Ponte Castañeda %T Second-order theory for nonlinear composites and application to isotropic constituents %J Comptes Rendus. Mécanique %D 2006 %P 575-581 %V 334 %N 10 %I Elsevier %R 10.1016/j.crme.2006.06.006 %G en %F CRMECA_2006__334_10_575_0
Martín I. Idiart; Kostas Danas; Pedro Ponte Castañeda. Second-order theory for nonlinear composites and application to isotropic constituents. Comptes Rendus. Mécanique, Volume 334 (2006) no. 10, pp. 575-581. doi : 10.1016/j.crme.2006.06.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.06.006/
[1] Nonlinear composites, Adv. Appl. Mech., Volume 34 (1998), pp. 171-302
[2] Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids, Volume 50 (2002), pp. 737-757
[3] Second-order estimates for nonlinear isotropic composites with spherical voids and rigid particles, C. R. Mecanique, Volume 333 (2005), pp. 147-154
[4] M.I. Idiart, P. Ponte Castañeda, Field statistics in nonlinear composites I. Theory, Proc. R. Soc. Lond. A (2006), in press
[5] A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization, C. R. Mecanique, Volume 333 (2005), pp. 789-795
[6] Macroscopic behavior and field fluctuations for viscoplastic composites: Second-order estimates versus full-field simulations, J. Mech. Phys. Solids, Volume 54 (2006), pp. 1029-1063
[7] Bounds and self-consistent estimates for the overall moduli of anisotropic composites, J. Mech. Phys. Solids, Volume 25 (1977), pp. 185-202
[8] The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids, Volume 39 (1991), pp. 45-71
[9] High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior, J. Mech. Phys. Solids, Volume 50 (2002), pp. 2577-2595
Cité par Sources :
Commentaires - Politique
A homogenization-based constitutive model for two-dimensional viscoplastic porous media
Kostas Danas; Martin I. Idiart; Pedro Ponte Castañeda
C. R. Méca (2008)
Second-order estimates for nonlinear isotropic composites with spherical pores and rigid particles
Martín Idiart; Pedro Ponte Castañeda
C. R. Méca (2005)
Nonlinear sequential laminates reproducing hollow sphere assemblages
Martín I. Idiart
C. R. Méca (2007)