Comptes Rendus
no. 1-2
Eigenspectra and orders of stress singularity at a mode I crack tip for a power-law medium
[Spectre et ordre de la singularité de contrainte à la pointe d'une fissure chargée en mode I dans un milieu dont le comportement suit une loi exponentielle]
Larisa Stepanova1
1 Department of Mathematical Modelling in Mechanics, Samara State University, Akad. Pavlov str., 1, 443011, Samara, Russia
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 232-237.

Dans cette Note, on détermine le spectre de valeurs propres du champ de contrainte asymptotique au voisinage de l'extrémité d'une fissure, dans le cas d'un matériau à comportement non linéaire. Toutes les valeurs propres sont obtenues par une méthode de perturbation. L'analyse indique que la valeur propre du problème non linéaire est complètement déterminée par la valeur propre du problème linéaire et le coefficient de consolidation plastique.

In this Note eigenspectra and orders of singularity of the stress field near a mode I crack tip in a power-law material are discussed. The perturbation theory technique is employed to pose the required asymptotic solution. The whole set of eigenvalues is obtained. It is shown that the eigenvalues of the nonlinear problem are fully determined by the corresponding eigenvalues of the linear problem and by the hardening exponent.

Publié le :
DOI : 10.1016/j.crme.2007.11.014
Keywords: Rupture, Fracture mechanics, Asymptotic analysis, Nonlinear eigenvalue problem
Mot clés : Rupture, Analyse asymptotique, Problème non linéaire aux valeurs propres
Larisa Stepanova 1

1 Department of Mathematical Modelling in Mechanics, Samara State University, Akad. Pavlov str., 1, 443011, Samara, Russia 
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Larisa Stepanova. Eigenspectra and orders of stress singularity at a mode I crack tip for a power-law medium. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 232-237. doi : 10.1016/j.crme.2007.11.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.014/

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