The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity

Details The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity

2011-10-21

arxiv.org/abs/1110.4796v2

Mathematics

Numerical Analysis

(version 2 : r\'ef\'erences corrig\'ees)

Scientific paper

Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution $u$ of a Neumann problem near a crack in dimension 2. We consider non smooth cracks $K$ that are merely closed and connected. At any point of density 1/2 in $K$, we show that the blow-up limit of $u$ is the usual "cracktip" function $\sqrt{r}\sin(\theta/2)$, with a well-defined coefficient (the "stress intensity factor" or SIF). The method relies on Bonnet's monotonicity formula \cite{b} together with $\Gamma$-convergence techniques.

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