Calculus of Variations and Geometric Measure Theory

A. Chambolle - A. Lemenant

The stress intensity factor for non-smooth fractures in antiplane elasticity

created by lemenant on 24 Nov 2011
modified on 10 Feb 2015


Published Paper

Inserted: 24 nov 2011
Last Updated: 10 feb 2015

Journal: Calc. Var. PDE
Year: 2013


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 12 in K , we show that the blow-up limit of u is the usual "cracktip" function, with a well-defined coefficient (the "stress intensity factor" or SIF). The method relies on Bonnet's monotonicity formula together with Γ-convergence techniques.