Comptes Rendus
A damage model based on singular elastic fields
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 283-288.

At re-entrant corners in elastic structures, the stress field is known to increase to infinity following a power law. From the material viewpoint it is paradoxical that it can locally sustain such an overburden. To avoid this paradox we propose a damage model where the Young's modulus of the material decreases (damage) also following a power law and such that the resulting stress field remains bounded.

Aux points anguleux rentrants d'une structure élastique, il est bien connu que les contraintes deviennent infinies en suivant une loi puissance. Du point de vue du matériau, il est paradoxal que celui-ci puisse supporter localement une telle surcharge. Pour éviter ce paradoxe, nous proposons un modèle d'endommagement dans lequel le module d'Young du matériau décroît (endommagement) en suivant également une loi puissance telle que le champ de contraintes résultant reste borné.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.10.011
Keywords: Damage, Elasticity, Singularities
Mot clés : Endommagement, Elasticité, Singularités

Dominique Leguillon 1

1 Institut Jean Le Rond d'Alembert, CNRS UMR 7190, Université Pierre et Marie Curie, case 162, 4, place Jussieu, 75252 Paris cedex 05, France
@article{CRMECA_2008__336_3_283_0,
     author = {Dominique Leguillon},
     title = {A damage model based on singular elastic fields},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {283--288},
     publisher = {Elsevier},
     volume = {336},
     number = {3},
     year = {2008},
     doi = {10.1016/j.crme.2007.10.011},
     language = {en},
}
TY  - JOUR
AU  - Dominique Leguillon
TI  - A damage model based on singular elastic fields
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 283
EP  - 288
VL  - 336
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2007.10.011
LA  - en
ID  - CRMECA_2008__336_3_283_0
ER  - 
%0 Journal Article
%A Dominique Leguillon
%T A damage model based on singular elastic fields
%J Comptes Rendus. Mécanique
%D 2008
%P 283-288
%V 336
%N 3
%I Elsevier
%R 10.1016/j.crme.2007.10.011
%G en
%F CRMECA_2008__336_3_283_0
Dominique Leguillon. A damage model based on singular elastic fields. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 283-288. doi : 10.1016/j.crme.2007.10.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.011/

[1] D. Leguillon; E. Sanchez-Palencia Computation of Singular Solutions in Elliptic Problems and Elasticity, John Wiley & Sons/Masson, New York/Paris, 1987

[2] J. Lemaître; J.L. Chaboche Mécanique des matériaux solides, Dunod, Paris, 1985

[3] T. Apel; V. Mehrmann; D. Watkins Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elastic structures, Comput. Methods Appl. Mech. Engrg., Volume 191 (2002), pp. 4459-4473

[4] J.W. Hutchinson Singular behaviour at the end of a tensile crack in a hardening material, J. Mech. Phys. Solids, Volume 16 (1968), pp. 13-31

[5] J.R. Rice; G.F. Rosengren Plane strain deformation near a crack tip in a power-law hardening material, J. Mech. Phys. Solids, Volume 16 (1968), pp. 1-12

[6] D. Leguillon Calcul du taux de restitution de l'énergie au voisinage d'une singularité, C. R. Acad. Sci. Paris, Série II, Volume 309 (1989), pp. 945-950

[7] P. Lazzarin; R. Zambardi A finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp V-shaped notches, Int. J. Fract., Volume 112 (2001), pp. 275-298

[8] P. Livieri; P. Lazzarin Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy, Int. J. Fract., Volume 133 (2005), pp. 247-276

[9] T. Boukharouba; T. Tamine; L. Niu; C. Chehimi; G. Pluvinage The use of notch stress intensity factor as a fatigue crack initiation parameter, Engrg. Fracture Mech., Volume 52 (1995) no. 3, pp. 503-512

Cited by Sources:

Comments - Policy