2011/10/21 by Antonin Chambolle, Antoine Lemenant, Chambolle, Antonin +1
Computer Science · Engineering · #Composite Material Mechanics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1110.4796
openalex publication_date 2011/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Motivated by some questions arising in the study of quasistatic growth in\nbrittle fracture, we investigate the asymptotic behavior of the energy of the\nsolution u of a Neumann problem near a crack in dimension 2. We consider non\nsmooth cracks K that are merely closed and connected. At any point of density\n1/2 in K, we show that the blow-up limit of u is the usual "cracktip"\nfunction \√(r)\sin(\θ/2), with a well-defined coefficient (the "stress\nintensity factor" or SIF). The method relies on Bonnet's monotonicity formula\n citeb together with \Γ-convergence techniques.\n