Numerical implementation of the variational formulation for quasi-static brittle fracture

By Blaise Bourdin. 2007

410 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/dee7cb47e35b8d13f81948934903f3d43a2b4b90

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional (2013, positive): “We will compare the monotonicity condition proposed in this paper with the Dirichlet condition used in [15], which was originally proposed by Bourdin [8].”
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models (2011, positive): “The main advantages of the variational approach are to give a unified setting for the analysis of existence, uniqueness and stability of quasi-static solutions and their numerical treatment (Bourdin, 2007; Amor et al., 2009).”
Phase-field modeling of fracture in linear thin shells (2014, positive): “In this model, cracks can propagate, branch and merge but can not reverse, whereas the last feature is reached by imposing υ 6 υi−1, such that υi−1 and υ are the phase-field parameters at step i− 1 and i [47].”
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure (2015, positive): “It has been adapted to quasi-static fracture problems in [9,8], dynamic crack propagation [11,27], and in a multiphysic context in [39,1].”
On penalization in variational phase-field models of brittle fracture (2018, methodology): “The regularization of (1) á la Bourdin-Francfort-Marigo [2, 3, 4, 5], which is the basis for a variety of fracture phase-field formulations, reads as follows: E(u, α) = ∫ Ω g(α)Ψ(ε(u)) dx︸︷︷︸ Eel.”
Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions (2012, background): “Requiring the field v to be a monotonically decreasing function of time is cumbersome, and in practice, the field v is frozen to 0 when and where it reaches a given small threshold g (Bourdin, 2007; Bourdin et al., 2008).”
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework (2014, methodology): “Although it has been used in numerous numerical implementations and theoretical papers (see Bellettini and Coscia [4], Bourdin [7], Bourdin, Francfort, and Marigo [9], Giacomini [20], Bourdin [8], Del Piero, Lancioni, and March [17], Lancioni and Royer-Carfagni [25], Amor, Marigo, and Maurini [2], B”
A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations (2015, methodology): “In numerical simulations theweaker conditionh < l is often adopted (Piero et al., 2007; Bourdin, 2007; Bourdin et al., 2008; Amor et al., 2009; Miehe et al., 2010a; Kuhn and Müller, 2010; Borden et al., 2012, 2014).”
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach (2015, methodology): “To address directly the numerical solution of the non-convex energy functional by minimization, the alternate minimization algorithm with backtracking was suggested in [3, 27].”
The Variational Approach to Fracture Mechanics. A Practical Application to the French Panthéon in Paris (2009, methodology): “9 By performing a stability analysis as in [ 7 ], one can find that in a uniaxial tensile test the material cannot sustain a stress greater than the critical value σc = a(γ μ/e)0.5, where a is a numerical coefficient.”
An overview of the modelling of fracture by gradient damage models (2016, neutral): “We refer to [11] and [17] for further details and extensions of the algorithm.”