Cet article retrace les grandes lignes de l’évolution des idées qui ont prévalu et des choix qui ont été faits dans la modélisation de la rupture des matériaux et des structures depuis un siècle. En particulier l’accent est mis sur la création et le développement de la mécanique de l’endommagement avec son ambition première de remédier aux lacunes de la théorie de la rupture de Griffith. On souligne les succès de cette entreprise et les avancées qu’elle a permises en insistant sur le rôle clé qu’a joué l’approche variationnelle, mais on montre aussi ses limites.
This article traces the main lines of the evolution of the ideas that have prevailed and the choices that have been made in modelling the fracture of materials for a century. In particular, the emphasis is on the creation and development of damage mechanics with its primary ambition to remedy the shortcomings of Griffith’s fracture theory. We underline the successes of this enterprise and the advances it has allowed by insisting on the key role played by the variational approach, but we also show its limits.
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Keywords: Damage, Fracture, Calculus of Variations, stability, free discontinuities
CC-BY 4.0
@article{CRMECA_2023__351_S3_A3_0,
author = {Jean-Jacques Marigo},
title = {La m\'ecanique de l{\textquoteright}endommagement au secours de la m\'ecanique de la rupture~~: l{\textquoteright}\'evolution de cette id\'ee en un demi-si\`ecle},
journal = {Comptes Rendus. M\'ecanique},
publisher = {Acad\'emie des sciences, Paris},
year = {2023},
doi = {10.5802/crmeca.156},
language = {fr},
note = {Online first},
}
TY - JOUR AU - Jean-Jacques Marigo TI - La mécanique de l’endommagement au secours de la mécanique de la rupture : l’évolution de cette idée en un demi-siècle JO - Comptes Rendus. Mécanique PY - 2023 PB - Académie des sciences, Paris N1 - Online first DO - 10.5802/crmeca.156 LA - fr ID - CRMECA_2023__351_S3_A3_0 ER -
%0 Journal Article %A Jean-Jacques Marigo %T La mécanique de l’endommagement au secours de la mécanique de la rupture : l’évolution de cette idée en un demi-siècle %J Comptes Rendus. Mécanique %D 2023 %I Académie des sciences, Paris %Z Online first %R 10.5802/crmeca.156 %G fr %F CRMECA_2023__351_S3_A3_0
Jean-Jacques Marigo. La mécanique de l’endommagement au secours de la mécanique de la rupture : l’évolution de cette idée en un demi-siècle. Comptes Rendus. Mécanique, Online first (2023), pp. 1-21. doi : 10.5802/crmeca.156.
[1] The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. Lond., Ser. A, Volume 221 (1921), pp. 163-198
[2] The mathematical theory of equilibrium cracks in brittle fracture (Advances in Applied Mechanics), Volume 7, Elsevier, 1962, pp. 55-129 | DOI
[3] Introduction to continuum damage mechanics, Mechanics of Elastic Stability, 10, Martinus Nijhoff Publishers, 1986 | DOI | Zbl
[4] Constitutive relations in Plasticity, Damage and Fracture Mechanics based on a Work Property, Nucl. Eng. Des., Volume 114 (1989) no. 3, pp. 249-272 | DOI
[5] Approximation of functionals depending on jumps by elliptic functional via Gamma-Convergence, Commun. Pure Appl. Math., Volume 43 (1990) no. 8, pp. 999-1036 | Zbl
[6] On the approximation of free discontinuity problems, Boll. Unione Mat. Ital., VII. Ser., B, Volume 6 (1992) no. 1, pp. 105-123 | MR | Zbl
[7] Evolution of rate-independent systems, Evolutionary equations. Vol. II (Handbook of Differential Equations), North-Holland, 2005, pp. 461-559 | Zbl
[8] Approche variationnelle de l’endommagement : I. Les concepts fondamentaux, C. R. Méc. Acad. Sci. Paris, Volume 338 (2010) no. 4, pp. 191-198 | Zbl
[9] Approche variationnelle de l’endommagement : II. Les modèles à gradient, C. R. Méc. Acad. Sci. Paris, Volume 338 (2010) no. 4, pp. 199-206 | Zbl
[10] An overview of the modelling of fracture by gradient damage models, Meccanica, Volume 51 (2016) no. 12, pp. 3107-3128 | MR | Zbl
[11] The variational approach to fracture, J. Elasticity, Volume 91 (2008) no. 1-3, pp. 5-148 | MR | Zbl
[12] Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, Volume 48 (2000) no. 4, pp. 797-826 | MR | Zbl
[13] Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces Free Bound., Volume 9 (2007) no. 3, pp. 411-430 | MR | Zbl
[14] From gradient damage laws to Griffith’s theory of crack, J. Elasticity, Volume 113 (2013) no. 1, pp. 55-74 | MR | Zbl
[15] Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks, Phys. Rev. Lett., Volume 112 (2014) no. 1, 014301, 5 pages | DOI
[16] Initiation of a periodic array of cracks in the thermal shock problem : a gradient damage modeling, J. Mech. Phys. Solids, Volume 63 (2014), pp. 256-284 | MR | Zbl
[17] Effect of crack pattern on the residual strength of ceramics after quenching, J. Am. Ceram. Soc., Volume 94 (2011) no. 9, pp. 2804-2807 | DOI
[18] Crack nucleation in variational phase-field models of brittle fracture, J. Mech. Phys. Solids, Volume 110 (2018), pp. 80-99 | DOI | MR
[19] Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., Volume 24 (1957) no. 3, pp. 361-364 | DOI
[20] Stable damage evolution in a brittle continuous medium, Eur. J. Mech., A, Solids, Volume 12 (1993) no. 2, p. 149--189 | MR | Zbl
[21] Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, Volume 46 (1998) no. 8, pp. 1319-1342 | MR | Zbl
[22] Existence of strong solutions to the Dirichlet problem for the Griffith energy, Calc. Var. Partial Differ. Equ., Volume 58 (2019) no. 4, 136, 27 pages | MR | Zbl
[23] A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., Volume 35 (1968) no. 2, pp. 379-386 | DOI
[24] Mathematical Analysis in the Mechanics of Fracture, Fracture : An Advanced Treatise (H. Liebowitz, ed.) (Mathematical Fundamentals), Volume 2, Academic Press Inc., 1968, pp. 191-311 | Zbl
[25] Sur une interprétation mathématique de l’intégrale de Rice en théorie de la rupture fragile, Math. Methods Appl. Sci., Volume 3 (1981) no. 1, pp. 70-87 | Zbl
[26] Mécanique des matériaux solides, Dunod, 1985
[27] A model of micro-craked material for concretes and rocks, J. Méc. Théor. Appl., Volume 5 (1986) no. 3, pp. 471-513 | Zbl
[28] Modelling of brittle and fatigue damage for elastic material by growth of microvoids, Eng. Fract. Mech., Volume 21 (1985) no. 4, pp. 861-874 | DOI
[29] Formulation d’une loi d’endommagement d’un matériau élastique, C. R. Acad. Sci., Sér. IIA Earth Planet. Sci., Volume 292 (1981) no. 19, pp. 1309-1312 | Zbl
[30] Sur les matériaux standards généralisés, J. Méc., Paris, Volume 14 (1975), pp. 39-63 | Zbl
[31] Non-local damage theory, J. Eng. Mech., Volume 113 (1987) no. 10, pp. 1512-1533 | DOI
[32] From damage to fracture mechanics and conversely : a combined approach, Int. J. Solids Struct., Volume 33 (1996) no. 20-22, pp. 3327-3342 | Zbl
[33] -convergence for Beginners, Oxford Lecture Series in Mathematics and its Applications, 22, Oxford University Press, 2002 | Zbl
[34] Fracture models as -limits of damage models, Commun. Pure Appl. Anal., Volume 12 (2013) no. 4, pp. 1657-1686 | MR | Zbl
[35] Gradient damage models and their use to approximate brittle fracture, Int. J. Damage Mech., Volume 20 (2011) no. 4, pp. 618-652
[36] Crack tip equation of motion in dynamic gradient damage models, J. Elasticity, Volume 127 (2017) no. 1, pp. 25-57 | MR | Zbl
[37] Fracture and healing of elastomers : A phase-transition theory and numerical implementation, J. Mech. Phys. Solids, Volume 112 (2018), pp. 523-551 | DOI | MR
[38] Regularized formulation of the variational brittle fracture with unilateral contact : Numerical experiments, J. Mech. Phys. Solids, Volume 57 (2009) no. 8, pp. 1209-1229 | Zbl
[39] Nucleation under multi-axial loading in variational phase-field models of brittle fracture, Int. J. Fract., Volume 237 (2022) no. 1-2, pp. 61-81 (Special Issue : Phase-Field Approaches in the 3rd Millenium) | DOI
[40] Gradient damage models applied to dynamic fragmentation of brittle materials, Int. J. Fract., Volume 220 (2019) no. 2, pp. 143-165 | DOI
[41] A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach, Comput. Methods Appl. Mech. Eng., Volume 361 (2020), 112731, 29 pages | MR | Zbl
[42] Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks, Arch. Ration. Mech. Anal., Volume 214 (2014) no. 2, pp. 575-615 | MR | Zbl
[43] Gradient damage models coupled with plasticity : variational formulation and main properties, Mech. Mater., Volume 80 (2015), pp. 351-367 | DOI
[44] Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity : the antiplane case, Calc. Var. Partial Differ. Equ., Volume 55 (2016) no. 3, 45, 39 pages | MR | Zbl
Cité par Sources :
Commentaires - Politique
Jean-Jacques Marigo
C. R. Méca (2023)
Yves Wadier; Eric Lorentz
C. R. Méca (2004)
Vers une théorie énergétique de la rupture fragile
Gilles Francfort; Jean-Jacques Marigo
C. R. Méca (2002)