Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

By Hanen Amor, Jean-Jacques Marigo, C. Maurini. 2009

1,545 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1ab979220bc4a016f2c3cb6670f38dae4c0f2ff0

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In Mechanics of Materials

Citations in the corpus

Phase-field modeling of ductile fracture (2015, neutral): “Two options for decomposition of e can be found in the literature, namely, the split into volumetric and deviatoric contributions, see [35], + e (ε) := 1 2 Kn〈tr(ε)〉(2)+ + μ(εdev : εdev), − e (ε) := 1 2 Kn〈tr(ε)〉(2)−, (6)”
Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions (2012, background): “…Arias (2011a,b, 2012) are based on variational theories of ferroelectric ceramics (Shu and Bhattacharya, 2001; Zhang and Bhattacharya, 2005; Su and Landis, 2007; Schrade et al., 2007) and brittle fracture (Francfort and Marigo, 1998; Bourdin et al., 2000, 2008; Bourdin, 2007; Amor et al., 2009).”
Phase field modelling of anisotropic crack propagation (2017, methodology): “This idea has been used in the regularized framework for brittle fracture of Amor et al. (2009) for isotropic case.”
Revisiting the problem of a crack impinging on an interface: A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model (2017, background): “Therefore, while in the bulk the fracture energy Gb c is dissipated according to the Griffith hypothesis [43], at the interface the corresponding fracture energy is released according to a cohesive zone formulation.”
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow (2018, methodology): “Two widely used approaches in the literature are: (1) to distinguish tensile and compressive principal strains [57], and (2) to distinguish the volumetric and deviatoric parts of the elastic strain tensor [56].”
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure (2015, positive): “Starting from the pioneering works of Francfort and Marigo [20], diﬃculties arising in the classical fracture framework can be overcome by a variational-based energy minimization framework for brittle fracture (see also [10,48,9,14,4]).”
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): “With minor modifications this approach has been adopted by, e.g.,Amor et al.(2009); Kuhn and Müller(2010); Miehe et al.(2010b); Borden et al. (2012).”
Phase-field modeling of fracture in linear thin shells (2014, neutral): “However, the computed surface energy will be slightly overestimated [28, 45].”
Phase-field modeling of hydraulic fracture (2016, background): “Examples of diffuse crack approaches include peridynamics([37,38]), gradient damage mechanics([39,40]), and the phase-field methods presented herein and by other recent studies([41-53]).”
Phase-field models for brittle and cohesive fracture (2014, positive): “This formulation was subsequently refined to account for the fact that damage evolution occurs under different straining modes [1, 4, 13, 17], and it was assumed that the elastic energy of the undamaged state can be additively decomposed into a damaged and an”