Comptes Rendus
no. 8
Computational modeling of material forming processes / Simulation numérique des procédés de mise en forme
A generalized anisotropic and asymmetric yield criterion with adjustable complexity
[Un critère d'écoulement plastique universel, anisotrope et asymétrique, avec complexité ajustable]
Christian Raemy1  ; Niko Manopulo1  ; Pavel Hora1
1 Institute of Virtual Manufacturing, Tannenstrasse 3, ETH Zurich, 8092 Zurich, Switzerland
Comptes Rendus. Mécanique, Volume 346 (2018) no. 8, pp. 779-793.

Au cours des dernières décennies, de nombreux modèles de critères d'écoulement plastique ont été présentés pour décrire le comportement des matériaux orthotropes présentant éventuellement une asymétrie entre la traction et la compression. Malheureusement, ils sont, soit exclusivement applicables à une seule classe de matériaux, soit d'une grande complexité. Le but de ce travail est de développer, pour des états de contraintes planes, un modèle universel et indépendant de la pression. Le critère d'écoulement plastique proposé est basé sur une série de Fourier bidimensionnelle. La complexité du modèle étant ajustable au nombre de coefficients de Fourier considérés, la quantité de données expérimentales prise en compte est donc illimitée, et ceci même en utilisant une loi d'écoulement associée. Cette fonction permet donc de modéliser un grand nombre de matériaux différents, avec ou sans asymétrie entre la traction et la compression.

During the past decades, numerous yield criteria for orthotropic materials, possibly showing tension–compression asymmetry, were developed. Although they were applied successfully to forming simulations, they are usually only adequate for a specific class of materials. The aim of this work is to present a generalized, pressure-independent criterion for plane stress states on the base of a two-dimensional Fourier series. Its complexity is adjustable through the number of considered Fourier coefficients, and thus, albeit using an associated flow rule, virtually any number of experimental data can be captured exactly. The criterion is applicable for materials with or without tension–compression asymmetry.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.05.002
Keywords: Anisotropy, Strength differential, Sheet metal forming, Differential geometry
Mot clés : Anisotropie, Asymétrie traction–compression, Formage de tôle, Géométrie différentielle
Christian Raemy 1 ; Niko Manopulo 1 ; Pavel Hora 1

1 Institute of Virtual Manufacturing, Tannenstrasse 3, ETH Zurich, 8092 Zurich, Switzerland 
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Christian Raemy; Niko Manopulo; Pavel Hora. A generalized anisotropic and asymmetric yield criterion with adjustable complexity. Comptes Rendus. Mécanique, Volume 346 (2018) no. 8, pp. 779-793. doi : 10.1016/j.crme.2018.05.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.05.002/

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