Numerical experiments in revisited brittle fracture

By Blaise Bourdin, Gilles A. Francfort, Jean-Jacques Marigo. 2000

2,607 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/28beb29432204f179101c3219cbb00ec21586af5

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In Mechanics of Materials

Citations in the corpus

A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach (2018, methodology): “Although alternatives are proposed in the literature [42–44], the present work is limited to the analysis of the well known relationship [18, 31, 38] g(d) = (1− d)(2) .”
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications (2019, background): “A sharp crack topology is recovered in the limit as l0 → 0 [30].”
Compactness and lower semicontinuity in $GSBD$ (2018, background): “1), which are used for the numerical simulations of evolutions in brittle fracture (such as in [9]), see [14] for details.”
Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures (2003, methodology): “Numerical computations concerning this model of evolution (see [7]) are performed using a discretization in time procedure and an approximation of the elastic energy proposed in 1990 by Ambrosio and Tortorelli (see [5],[6]).”
The Variational Approach to Fracture (2008, background): “critical load at which the alternate minimization bifurcates away from an elastic-type solution is higher than in the experiment in [22], since the regularization parameter ε is smaller.”
An overview of the modelling of fracture by gradient damage models (2016, positive): “It constitutes essentially a summary of the works devoted to the variational approach to fracture, starting from [19] and followed by several other papers like [12] where the first numerical tests using Ambrosio–Tortorelli’s model are presented, [38, 39] where a general method for the construction o”
A robust algorithm for configurational‐force‐driven brittle crack propagation with R‐adaptive mesh alignment (2007, background): “[19] and Negri [42] similar to finite element formulations of image segmentation.”
A phase‐field model for cohesive fracture (2013, methodology): “This formulation closely resembles that in [18].”
Phase-field description of brittle fracture in plates and shells (2016, methodology): “[5,6] who regularized the variational formulation of Griffith’s theory presented by Francfort and Marigo [7].”
A level set based model for damage growth: The thick level set approach (2011, neutral): “The phase-field approach emanating from the physics community [15–17] and the so-called variational approach [18–20].”
Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples (2017, positive): “The second term in the damage dissipation potential part can be recognised as the standard gradient-damage contribution to the brittle-fracture regularisation model, [23] , with ! > 0 having the role of an internal material length related to the width of a damage localisation profile.”