[Une revue des longueurs caractéristiques dans le cadre du critère couplé et dans les modèles de fracture avancés]
Cet article de revue explore l’importance des longueurs caractéristiques en mécanique de la rupture, en se concentrant sur le cadre du Critère Couplé. Il met en lumière les limites des approches traditionnelles de la mécanique de la rupture élastique linéaire, qui peinent à prédire les comportements des fissures à petite échelle, et souligne le besoin de modèles permettant aux longueurs caractéristiques d’émerger des propriétés des matériaux et de la géométrie, plutôt que d’être définies a priori.
La revue couvre deux longueurs caractéristiques principales : la longueur de fissure d’initiation et la longueur d’Irwin, en examinant leurs interactions avec les longueurs utilisées dans d’autres approches de rupture, telles que les méthodes de champ de phase, les modèles de zone cohésive et les simulations à l’échelle atomique. Les résultats montrent que la longueur d’Irwin apparaît systématiquement dans les modèles combinant des critères de contrainte et énergétique, soulignant son rôle fondamental dans la prédiction de la rupture.
L’étude identifie les limites des modèles actuels, en particulier dans les cas impliquant des singularités fortes ou lorsque la condition énergétique domine, et propose des améliorations en incorporant des descriptions de zone de processus ou des techniques de régularisation issues des modèles de champ de phase. Ces améliorations pourraient mieux capturer les comportements complexes à des plus petites échelles.
L’article conclut en prônant une approche combinée intégrant divers modèles de rupture, ce qui pourrait offrir une compréhension plus complète de l’initiation et de la propagation des fissures à différentes échelles. Cette stratégie intégrative permettrait des prédictions plus précises et une compréhension approfondie des mécanismes de la rupture.
The review paper explores the significance of characteristic lengths in fracture mechanics, focusing on the Coupled Criterion framework. It addresses limitations in traditional Linear Elastic Fracture Mechanics, which struggle to predict small-scale crack behaviors, and highlights the need for models that allow characteristic lengths to emerge from material properties and geometry rather than being predefined inputs.
The review covers two main characteristic lengths: the initiation crack length and Irwin’s length, examining their interactions with lengths used in other fracture approaches such as Phase-Field methods, Cohesive Zone Models, and atomic-scale simulations. The findings show that Irwin’s length consistently appears in models that combine stress and energy criteria, indicating its fundamental role in fracture prediction.
The study identifies limitations in current models, especially in cases involving strong singularities or where the energy condition dominates, and suggests improvements by incorporating process zone descriptions or regularization techniques from Phase-Field models. These enhancements could better capture the complex behaviors at smaller scales.
The paper concludes by advocating for a combined approach that integrates various fracture models, which could provide a more comprehensive understanding of crack initiation and propagation across different scales. This integrative strategy would allow for more accurate predictions and a deeper insight into the mechanics of fracture.
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Mots-clés : Mécanique de la rupture finie, Critère couplé, Longueur caractéristique, Initiation de fissure, Longueur d’Irwin
Gergely Molnár 1 ; Aurélien Doitrand 2 ; Rafael Estevez 3 ; Anthony Gravouil 4
CC-BY 4.0
@article{CRMECA_2025__353_G1_91_0,
author = {Gergely Moln\'ar and Aur\'elien Doitrand and Rafael Estevez and Anthony ~Gravouil},
title = {A review of characteristic lengths in the coupled criterion framework and advanced fracture models},
journal = {Comptes Rendus. M\'ecanique},
pages = {91--111},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
year = {2025},
doi = {10.5802/crmeca.280},
language = {en},
}
TY - JOUR AU - Gergely Molnár AU - Aurélien Doitrand AU - Rafael Estevez AU - Anthony Gravouil TI - A review of characteristic lengths in the coupled criterion framework and advanced fracture models JO - Comptes Rendus. Mécanique PY - 2025 SP - 91 EP - 111 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.280 LA - en ID - CRMECA_2025__353_G1_91_0 ER -
%0 Journal Article %A Gergely Molnár %A Aurélien Doitrand %A Rafael Estevez %A Anthony Gravouil %T A review of characteristic lengths in the coupled criterion framework and advanced fracture models %J Comptes Rendus. Mécanique %D 2025 %P 91-111 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.280 %G en %F CRMECA_2025__353_G1_91_0
Gergely Molnár; Aurélien Doitrand; Rafael Estevez; Anthony Gravouil. A review of characteristic lengths in the coupled criterion framework and advanced fracture models. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 91-111. doi : 10.5802/crmeca.280. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.280/
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