Existence and convergence for quasi‐static evolution in brittle fracture

By Gilles A. Francfort, Christopher J. Larsen. 2003

217 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/07973999cf63740d9425e341d74f767f12d7f0d6

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Quasi-static crack growth for a cohesive zone model with prescribed crack path (2005, methodology): “For this reason we cannot apply directly the tools developed so far in the applications to fracture mechanics of the theory of free discontinuity problems (see [10], [5], [6], [1], [9], [3], [4]).”
A time-discrete model for dynamic fracture based on crack regularization (2011, background): “As in Francfort and Larsen (2003), we enforce boundary conditions by considering an extended domain !”
An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional (2013, unknown): “(4) For further details of the model and the existence of solutions in both the time-discrete form and as ∆t→ 0 we refer to [3, 20, 21, 25, 26].”
The Variational Approach to Fracture (2008, background): “This is the essence of the jump transfer theorem [52], Section 2.”
An approximation result for special functions with bounded deformation (2004, background): “Does each minimization problem have a solution? Does there exist some limit evolution as δt ↓ 0? Some of these issues are addressed in [3, 18, 16, 21, 17], for variants of this problem (scalar versions, topological restrictions on the cracks, nonlinear elasticity).”
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments (2009, background): “D antiplane shear, by Francfort and Larsen (2003) for the n-dimensional case including cracks with an arbitrary number of connected components, and by Chambolle (2003, 2004) for plane elasticity with vectorial displacement fields.”
Quasistatic Crack Growth in Nonlinear Elasticity (2005, methodology): “Larsen, his co-author for [17], and his invaluable contribution to the subject.”
Generalised functions of bounded deformation (2013, background): “In the antiplane case (see [20]), u is a scalar function on and the L bound is obtained by truncation, assuming that the prescribed boundary values are bounded in L.”
When and how do cracks propagate? (2009, unknown): “Of course, energy conservation needs to be re-formulated in such a framework (see [11, 14, 4, 13]).”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “As mentioned in the introduction, the proof puts the new ideas of a similar existence result for quasi-static brittle fracture evolution [11], [14] into the more general context of abstract rate-independent models, as studied in [25].”
Existence results for energetic models for rate-independent systems (2005, methodology): “Moreover, we show that the model of brittle fracture introduced in [FrM93] and developed further in [FrM98, DaT02, Cha03, FrL03 ] is a special case of our theory.”
A Γ-Convergence Approach to Stability of Unilateral Minimality Properties in Fracture Mechanics and Applications (2006, methodology): “1 also holds in the following discretized in time version, which is closer in spirit to the approach of Francfort and Marigo [22] to quasistatic crack propagation, and of the subsequent papers on the subject ([1], [16], [18], [19], [21], [23] and [24]).”
Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures (2003, background): “,k [ul(x)] > 1 j  , where E a and Ak are defined as the corresponding sets for u(t), following [14], we cover Jj in such a way that for all xi ∈ Jj there exists l with xi ∈ Su(tl) and HN−1  ⋃ r=1,.”
Epsilon‐stable quasi‐static brittle fracture evolution (2009, methodology): “Note that with global minimality, there is no issue of accessibility, and the stability of u when un are stable is exactly the point of the Jump Transfer method we introduced in [8].”