Convergence analysis for a smeared crack approach in brittle fracture
Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 307-330
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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 Gh (being h the element size) which accounts both for elastic displacements and fractures. Our main interest is the behaviour of Gh as h→0. We prove that, only for a suitable choice of the (mesh dependent) constitutive law, Gh converges to a limit functional Gφ 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.
Classification :
35-XX, 65-XX, 76-XX, 92-XX
Affiliations des auteurs :
Matteo Negri 1
Matteo Negri. Convergence analysis for a smeared crack approach in brittle fracture. Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 307-330. doi: 10.4171/ifb/166
@article{10_4171_ifb_166,
author = {Matteo Negri},
title = {Convergence analysis for a smeared crack approach in brittle fracture},
journal = {Interfaces and free boundaries},
pages = {307--330},
year = {2007},
volume = {9},
number = {3},
doi = {10.4171/ifb/166},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/166/}
}
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