The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity

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.