# 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

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topCostabel, 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 -

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