On a variational,free-discontinuity formulation of brittle fracture: mean-field relaxation and numerical solution

In this paper we address the resolution of two important issues arising in the context of the relaxed variational formulation of the incremental free–boundary value problem of brittle fracture. First issue, is how by recasting the formulation into a discrete, minimum–maximum problem one can avoid the undesirable scale effects expressed in terms of the characteristic size and domain–shape dependence of the calculated minimum; second, how by a remeshing procedure in combination with a domain–shape update for tracking the propagating 0–th level set one can reconstruct the crack surface. We finally illustrate our approach by a geometrically linear 2–dimensional example for crack propagation in an initially isotropic brittle solid. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)