Analysis of crack singularities in an aging elastic material

Martin Costabel; Monique Dauge; SergeïA. Nazarov; Jan Sokolowski

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 3, page 553-595
  • ISSN: 0764-583X

Abstract

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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 1 2 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.

How to cite

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Costabel, Martin, et al. "Analysis of crack singularities in an aging elastic material." ESAIM: Mathematical Modelling and Numerical Analysis 40.3 (2006): 553-595. <http://eudml.org/doc/249733>.

@article{Costabel2006,
abstract = { 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. },
author = {Costabel, Martin, Dauge, Monique, Nazarov, SergeïA., Sokolowski, Jan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Crack singularities; creep theory; Volterra kernel; hereditarily-elastic.; asymptotic solution; anisotropic material law},
language = {eng},
month = {7},
number = {3},
pages = {553-595},
publisher = {EDP Sciences},
title = {Analysis of crack singularities in an aging elastic material},
url = {http://eudml.org/doc/249733},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Costabel, Martin
AU - Dauge, Monique
AU - Nazarov, SergeïA.
AU - Sokolowski, Jan
TI - Analysis of crack singularities in an aging elastic material
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/7//
PB - EDP Sciences
VL - 40
IS - 3
SP - 553
EP - 595
AB - 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.
LA - eng
KW - Crack singularities; creep theory; Volterra kernel; hereditarily-elastic.; asymptotic solution; anisotropic material law
UR - http://eudml.org/doc/249733
ER -

References

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