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The variational formulation of brittle fracture: numerical implementation and extensions. (English) Zbl 1209.74036
Combescure, Alain (ed.) et al., IUTAM symposium on discretization methods for evolving discontinuities. Proceedings of the IUTAM symposium held in Lyon, France, September 4–7, 2006. Dordrecht: Springer (ISBN 978-1-4020-6529-3/hbk). IUTAM Bookseries 5, 381-393 (2007).
Summary: This paper presents the implementation of a variational formulation of brittle fracture mechanics proposed by G. A. Francfort and J.-J. Marigo [J. Mech. Phys. Solids 46, No.8, 1319–1342 (1998; Zbl 0966.74060)]. The essence of the model relies on successive global minimizations of an energy with respect to any crack set and any kinematically admissible displacement field. We briefly present the model itself, and its variational approximation in the sense of gamma-convergence. We propose a globally convergent and monotonically decreasing numerical algorithm. We introduce a backtracking algorithm whose solution satisfy a global optimality criterion with respect to the time evolution. We illustrate this algorithm with three dimensional numerical experiments. Then we present an extension of the model to crack propagation under thermal load and its numerical application to the quenching of glass.
For the entire collection see [Zbl 1124.74002].

MSC:
74R10 Brittle fracture
74G65 Energy minimization in equilibrium problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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