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| HAL : hal-00012082, version 1 |
| DOI : 10.1051/m2an:2006022 |
| Fiche détaillée |  Récupérer au format |
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| ESAIM: Mathematical Modelling and Numerical Analysis 40, 3 (2006) 553-595 |
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| Analysis of crack singularities in an aging elastic material |
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| Martin Costabel 1Monique Dauge 1 |
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| (2006) |
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| We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel, these asymptotics contain singular functions which are simple homogeneous functions of degree \frac12 or have a more complicated dependence on the distance variable r to the crack tips. In the latter situation, we observe a novel behavior of the singular functions, incompatible with the usual fracture criteria, involving super polynomial functions of \ln(r) growing in time. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2 : | Institute of Mechanical Engineering Problems (IPME) |
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Russian Academy of Science |
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| 3 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Physique/Mécanique/Mécanique des structures Sciences de l'ingénieur/Mécanique/Mécanique des structures |
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| Crack singularities – creep theory – Volterra kernel – hereditarily-elastic |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00012082, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00012082 | |
| oai:hal.archives-ouvertes.fr:hal-00012082 | |
| Contributeur : Monique Dauge | |
| Soumis le : Vendredi 14 Octobre 2005, 23:24:49 | |
| Dernière modification le : Vendredi 20 Janvier 2012, 14:05:11 | |
