Scaling in fracture mechanics by Ba\u17dant law: From finite to linearized elasticity

We consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains n\u3a9 on which the imposed boundary conditions scale according to Bazant's law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n \u2192 1e) to the evolution of a crack in a brittle linear-elastic materia