[Revue de l’approche asymptotique du critère couplé]
Les développements asymptotiques raccordés constituent une technique mathématique puissante, largement applicable dans divers domaines de l’ingénierie. L’une de leurs principales utilisations se situe en mécanique de la rupture, où ils permettent d’obtenir des approximations précises à proximité de la pointe des fissures tout en maintenant une faible complexité de calcul. Cette méthode peut être intégrée de manière fluide au critère couplé (CC), qui permet de prédire l’amorçage et la propagation des fissures dans les matériaux fragiles. Cet article explique comment la technique des développements asymptotiques raccordés peut être utilisée conjointement avec le critère couplé dans le cadre de la mécanique de la rupture, tout en offrant une revue détaillée de la littérature sur les avancées réalisées au cours de la dernière décennie.
Matched Asymptotics is a powerful mathematical technique with broad applicability in various engineering fields. One of its key uses is in Fracture Mechanics, where it provides accurate approximations in the vicinity of the crack tip with low computational complexity. This method can be seamlessly integrated with the Coupled Criterion (CC), which enables the prediction of crack nucleation and propagation in brittle materials. Hence, this paper deeply explains how the MA technique can be applied together with the CC in the context of Fracture Mechanics, providing a detailed literature review of the advances made in the last decade.
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Mots-clés : Développement asymptotique raccordé, Critère couplé, Mécanique de la rupture
Sara Jiménez-Alfaro 1, 2 ; Israel García García 3 ; Aurélien Doitrand 4
CC-BY 4.0
@article{CRMECA_2025__353_G1_339_0,
author = {Sara Jim\'enez-Alfaro and Israel Garc{\'\i}a Garc{\'\i}a and Aur\'elien Doitrand},
title = {Review of the matched asymptotic approach of the coupled criterion},
journal = {Comptes Rendus. M\'ecanique},
pages = {339--357},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
year = {2025},
doi = {10.5802/crmeca.285},
language = {en},
}
TY - JOUR AU - Sara Jiménez-Alfaro AU - Israel García García AU - Aurélien Doitrand TI - Review of the matched asymptotic approach of the coupled criterion JO - Comptes Rendus. Mécanique PY - 2025 SP - 339 EP - 357 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.285 LA - en ID - CRMECA_2025__353_G1_339_0 ER -
%0 Journal Article %A Sara Jiménez-Alfaro %A Israel García García %A Aurélien Doitrand %T Review of the matched asymptotic approach of the coupled criterion %J Comptes Rendus. Mécanique %D 2025 %P 339-357 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.285 %G en %F CRMECA_2025__353_G1_339_0
Sara Jiménez-Alfaro; Israel García García; Aurélien Doitrand. Review of the matched asymptotic approach of the coupled criterion. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 339-357. doi : 10.5802/crmeca.285. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.285/
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