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 or have a more complicated dependence on the distance variable 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 growing in time.
Mots-clés : crack singularities, creep theory, Volterra kernel, hereditarily-elastic
@article{M2AN_2006__40_3_553_0, author = {Costabel, Martin and Dauge, Monique and Nazarov, Serge{\"\i} A. and Sokolowski, Jan}, title = {Analysis of crack singularities in an aging elastic material}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {553--595}, publisher = {EDP-Sciences}, volume = {40}, number = {3}, year = {2006}, doi = {10.1051/m2an:2006022}, mrnumber = {2245321}, zbl = {1106.74028}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2006022/} }
TY - JOUR AU - Costabel, Martin AU - Dauge, Monique AU - Nazarov, Sergeï A. AU - Sokolowski, Jan TI - Analysis of crack singularities in an aging elastic material JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 553 EP - 595 VL - 40 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2006022/ DO - 10.1051/m2an:2006022 LA - en ID - M2AN_2006__40_3_553_0 ER -
%0 Journal Article %A Costabel, Martin %A Dauge, Monique %A Nazarov, Sergeï A. %A Sokolowski, Jan %T Analysis of crack singularities in an aging elastic material %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 553-595 %V 40 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2006022/ %R 10.1051/m2an:2006022 %G en %F M2AN_2006__40_3_553_0
Costabel, Martin; Dauge, Monique; Nazarov, Sergeï A.; Sokolowski, Jan. Analysis of crack singularities in an aging elastic material. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 3, pp. 553-595. doi : 10.1051/m2an:2006022. http://archive.numdam.org/articles/10.1051/m2an:2006022/
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