Asymptotics near crack tips in hereditarily-elastic anisotropic aging two dimensional body

Martin Costabel, Monique Dauge, Sergei A. Nazarov, Jan Sokolowski

A model involving a Volterra kernel is considered for a hereditarily-elastic anisotropic aging two-dimensional body with a straight crack. The asymptotics of the time dependent solution near the crack tips is investigated.

We prove that, depending on the regularity of the material law and the Volterra kernel, these asymptotics
- either have simple homogeneous behavior of degree 1/2 (in relation with the former results [1] and [2])
- or have a more complicated dependence on the distance variable r to the crack tips. In the latter situation, asymptotics involve a function of log r growing in time, which requires a modification of usual fracture criteria.

14 December 2004. Preprint IRMAR 04-57. Preprint IECN 59/2004.

M2AN Vol. 40, n° 3 (2006), pp 553-595.

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