Analysis of crack singularities in an aging elastic material

Martin Costabel (1) , Monique Dauge (1) , Sergei A. Nazarov (2) , Jan Sokolowski (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
3 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Crack singularities; creep theory; Volterra kernel; hereditarily-elastic

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Martin Costabel, Monique Dauge, Sergei A. Nazarov, Jan Sokolowski. Analysis of crack singularities in an aging elastic material. ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (3), pp.553-595. ⟨10.1051/m2an:2006022⟩. ⟨hal-00012082⟩