[On the ‘isotropic’ and ‘anisotropic’ approximations of the tangent operator in the incremental tangent and affine methods]
Three localisation rules, TFA, the incremental tangent, and the affine method, are recalled and evaluated in the context of the elastoplastic micromechanical analysis of heterogeneous materials, composites or polycrystals. With the help of a severe example, it is shown how methods based on the complete anisotropic elastoplastic tangent operator yield very stiff predictions which are far from the reference solution; the same conclusion holds for the method using the elastic accommodation rule. On the other hand, using an isotropic form of the tangent operator delivers much better responses. The reasons for such differences are discussed, together with possible justifications for the choice of the isotropic form.
Trois règles de localisation, TFA, la méthode tangente incrémentale et la méthode affine, sont rappelées et évaluées dans le contexte de l'analyse micromécanique de l'élastoplasticité des matériaux hétérogènes, composites ou polycristaux. A l'aide d'un exemple sévère, on montre comment les prédictions issues des méthodes basées sur l'expression anisotrope complète de l'opérateur élastoplastique tangent sont très raides et éloignées de la réponse de référence, tout comme pour la méthode basée sur la règle d'accommodation élastique. Au contraire, en utilisant une forme isotrope de l'opérateur tangent, on obtient des réponses bien meilleures. Sont alors discutées les raisons d'une telle différence et les justifications possibles du choix de la forme isotrope.
Accepted:
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Keywords: Computation solid mechanics, TFA, Incremental tangent method, Affine method, Elastoplastic micromechanical analysis
Jean-Louis Chaboche 1; Pascale Kanouté 1
@article{CRMECA_2003__331_12_857_0, author = {Jean-Louis Chaboche and Pascale Kanout\'e}, title = {Sur les approximations {\guillemotleft} isotrope {\guillemotright} et {\guillemotleft} anisotrope {\guillemotright} de l'op\'erateur tangent pour les m\'ethodes tangentes incr\'ementale et affine}, journal = {Comptes Rendus. M\'ecanique}, pages = {857--864}, publisher = {Elsevier}, volume = {331}, number = {12}, year = {2003}, doi = {10.1016/j.crme.2003.08.002}, language = {fr}, }
TY - JOUR AU - Jean-Louis Chaboche AU - Pascale Kanouté TI - Sur les approximations « isotrope » et « anisotrope » de l'opérateur tangent pour les méthodes tangentes incrémentale et affine JO - Comptes Rendus. Mécanique PY - 2003 SP - 857 EP - 864 VL - 331 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2003.08.002 LA - fr ID - CRMECA_2003__331_12_857_0 ER -
%0 Journal Article %A Jean-Louis Chaboche %A Pascale Kanouté %T Sur les approximations « isotrope » et « anisotrope » de l'opérateur tangent pour les méthodes tangentes incrémentale et affine %J Comptes Rendus. Mécanique %D 2003 %P 857-864 %V 331 %N 12 %I Elsevier %R 10.1016/j.crme.2003.08.002 %G fr %F CRMECA_2003__331_12_857_0
Jean-Louis Chaboche; Pascale Kanouté. Sur les approximations « isotrope » et « anisotrope » de l'opérateur tangent pour les méthodes tangentes incrémentale et affine. Comptes Rendus. Mécanique, Volume 331 (2003) no. 12, pp. 857-864. doi : 10.1016/j.crme.2003.08.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.08.002/
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