Quasistatic Crack Growth in Nonlinear Elasticity

By Gianni Dal Maso, Gilles A. Francfort, Rodica Toader. 2005

345 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f20674db64baefbcae6643977d358b05ed5c1ae3

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

WELL-POSEDNESS AND LONG-TIME BEHAVIOR FOR A CLASS OF DOUBLY NONLINEAR EQUATIONS (2006, background): “1) stem in connection with phase change phenomena [14, 17, 23, 32, 46, 47], gas flow through porous media [68], damage [15, 16, 30, 31, 54], and, in the specific case α(λr) = α(r) for all λ > 0 and r ∈ R (which is however not included in the present analysis), elastoplasticity [25, 50, 51, 52], brit”
The Variational Approach to Fracture (2008, background): “Our narration of the variational evolution is mathematically precise, but an overload of technicalities would serve no useful purpose and the curious reader may wish to consult [40] on this issue.”
Epsilon‐stable quasi‐static brittle fracture evolution (2009, background): “Recent mathematical progress on fracture ([9], [5], [6], [8], [4]) is based on an attempt to turn Griffith’s criterion for crack growth into a well-posed model for predicting crack paths, at least in the quasi-static case (by “well-posed” we mean that existence can be shown – “Only a mathematical ex”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, methodology): “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].”
Γ-limits and relaxations for rate-independent evolutionary problems (2008, methodology): “The construction of the limit function φ : [0, T ] → F is more involved and follows [13].”
Generalised functions of bounded deformation (2013, methodology): “In the vector case, the solution adopted in [16, 17] is to formulate the problems in the larger space GSBV(;R), defined as the set of all L-measurable functions u : → R such that ψ(u) ∈ BVloc(;R) for every ψ ∈ C1(Rn;Rn) such that ∇ψ has compact support.”
A Γ-Convergence Approach to Stability of Unilateral Minimality Properties in Fracture Mechanics and Applications (2006, background): “Then we have immediately that the pair (u,K) is a unilateral minimizer for f and g because for all pairs (v,H) with S(v) ⊆ H and K ⊆ H we have ∫ Ω f(x,∇u(x)) dx = E(u) ≤ E(v) = ∫ Ω f(x,∇v(x)) dx + ∫ S(v) g−(x, ν) dHN−1 = ∫ Ω f(x,∇v(x)) dx + ∫ S(v)\K g−(x, ν) ≤ ∫ Ω f(x,∇v(x)) dx + ∫ H\K g(x, ν).”
Fractional Piola identity and polyconvexity in fractional spaces (2018, neutral): “, [4, 25, 10, 18]).”
An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional (2013, neutral): “(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].”
Quasi-static crack growth for a cohesive zone model with prescribed crack path (2005, methodology): “Some tools We introduce a notion of convergence for the functions γ, which is the counterpart of the notion of convergence of sets introduced in [4].”