Abstract
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 \({C\sqrt{r}\sin(\theta/2)}\) , with a well-defined coefficient (the “stress intensity factor” or SIF). The method relies on Bonnet’s monotonicity formula (Bonnet, Variational methods for discontinuous structures, pp. 93–103. Birkhäuser, Basel, 1996) together with Γ-convergence techniques.
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Communicated by L. Ambrosio.
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Chambolle, A., Lemenant, A. The stress intensity factor for non-smooth fractures in antiplane elasticity. Calc. Var. 47, 589–610 (2013). https://doi.org/10.1007/s00526-012-0529-9
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DOI: https://doi.org/10.1007/s00526-012-0529-9