Gradient damage models: Toward full-scale computations

By E. Lorentz, V. Godard. 2011

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Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion (2020, background): “Though there are other methods to obtain a positive damage rate (e.g., bound constrained non-linear optimization techniques (Amor et al., 2009; Farrell and Maurini, 2017; Wu, 2018b), augmented Lagrangian (Lorentz and Godard, 2011; Wheeler et al., 2014) or penalization methods (Gerasimov and Lorenzis”
Modelling large crack propagation: from gradient damage to cohesive zone models (2012, background): “It appears well-suited for modelling large crack propagation, thanks to the following properties detailed in Lorentz and Godard (2011): –”
A phase-field formulation for dynamic cohesive fracture (2018, methodology): “Trapezoid problem We now examine a problem first proposed by Lorentz and Godard (2011) in which a particular geometric setup is designed to facilitate stable crack propagation without exhibiting any snap-back behavior.”
Double-phase-field formulation for mixed-mode fracture in rocks (2020, methodology): “Drawing on the gradient damage models of Lorentz and coworkers [30–32], these phase-field models have incorporated one-dimensional softening behavior through careful design of functions for geometric regularization and material degradation.”