Our analysis focuses on the mechanical energies involved in the propagation of fractures: the elastic energy, stored in the bulk, and the fracture energy, concentrated in the crack. We consider a finite element model based on a smeared crack approach: the fracture is approximated geometrically by a stripe of elements and mechanically by a softening constitutive law. We define in this way a discrete free energy (being the element size) which accounts both for elastic displacements and fractures. Our main interest is the behaviour of as . We prove that, only for a suitable choice of the (mesh dependent) constitutive law, converges to a limit functional with a positive (anisotropic) term concentrated on the crack. We discuss the mesh bias and compute it explicitly in the case of a structured triangulation.
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Matteo Negri, Convergence analysis for a smeared crack approach in brittle fracture. Interfaces Free Bound. 9 (2007), no. 3, pp. 307–330DOI 10.4171/IFB/166