The Variational Approach to Fracture Mechanics. A Practical Application to the French Panthéon in Paris

By G. Lancioni, G. Royer-Carfagni. 2009

181 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1c72c063f6af16541b090cba57fe200683de86ea

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In Mechanics of Materials

Citations in the corpus

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”
High-accuracy phase-field models for brittle fracture based on a new family of degradation functions (2017, background): “Lancioni and Royer-Carfagni (2009) adopted the above model to shear cracking by having g (φ) act only on the deviatoric portion of the strain.”
Gradient Damage Models and Their Use to Approximate Brittle Fracture (2011, unknown): “For further details on the numerical applications of the variational approach to brittle fracture and its extensions, the reader may refer to Del Piero et al. (2007), Amor et al. (2009), and Lancioni and Royer-Carfagni (2009).”
A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach (2018, background): “Although other options are available [44, 46, 47], the present work adopts the following choices:”
An overview of the modelling of fracture by gradient damage models (2016, unknown): “Nowadays the so-called phase-field models of fracture are extensively adopted in computational mechanics to study fracture phenomena [27, 20, 44, 26, 33, 10, 28].”
A time-discrete model for dynamic fracture based on crack regularization (2011, background): “One can also deviate from ideally brittle linear elastic materials and account for different elastic and fracture response under traction and compression, as in Lancioni and Royer-Carfagni (2009), for instance.”
Phase-field models for brittle and cohesive fracture (2014, unknown): “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”
An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional (2013, methodology): “Alternative methods for implementing crack irreversibility have been proposed [1,4,22,31]; a nice survey of these methods is provided in the paper by Amora, Marigo and Maurini [4, Page 1220].”
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments (2009, background): “One may try, at best, to look for the local minima around the solution at the previous time step (Bourdin et al., 2000; Del Piero et al., 2007; Lancioni and Royer-Carfagni, 2009).”
On penalization in variational phase-field models of brittle fracture (2018, methodology): “[7], Lancioni and Royer-Carfagni [8], Amor et al.”