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The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field.
Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process
Mark S. Shephard · 1984
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Optimal approximations by piecewise smooth functions and associated variational problems
David Bryant Mumford and Jayant Shah · 1989
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Revisiting brittle fracture as an energy minimization problem
G.A. Francfort and J.-J. Marigo · 1998
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Numerical experiments in revisited brittle fracture
B. Bourdin, G.A. Francfort, and J-J. Marigo · 2000
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Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials
Frédéric Feyel and Jean-Louis Chaboche · 2000
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Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement
Thomas JR Hughes, John A Cottrell, and Yuri Bazilevs · 2005
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Numerical implementation of the variational formulation for quasi-static brittle fracture
B. Bourdin · 2007
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A dissipation-based arc-length method for robust simulation of brittle and ductile failure
Clemens V. Verhoosel, Joris J. C. Remmers, and Miguel A. Gutiérrez · 2009
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Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field fe implementations
Christian Miehe, Fabian Welschinger, and Martina Hofacker · 2010
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A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
Christian Miehe, Martina Hofacker, and Fabian Welschinger · 2010
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Linear independence of the t-spline blending functions associated with some particular t-meshes
Annalisa Buffa, Durkbin Cho, and Giancarlo Sangalli · 2010
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On the performance of strain smoothing for quadratic and enriched finite element approximations (xfem/gfem/pufem)
Stéphane PA Bordas, Sundararajan Natarajan, Pierre Kerfriden, Charles Edward Augarde, D Roy Mahapatra, Timon Rabczuk, and Stefano Dal Pont · 2011
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Isogeometric finite element data structures based on bézier extraction of t-splines
Michael A Scott, Michael J Borden, Clemens V Verhoosel, Thomas W Sederberg, and Thomas JR Hughes · 2011
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Gradient damage models and their use to approximate brittle fracture
Kim Pham, Hanen Amor, Jean-Jacques Marigo, and Corrado Maurini · 2011
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Nonlinear finite element analysis of solids and structures
René De Borst, Mike A Crisfield, Joris JC Remmers, and Clemens V Verhoosel · 2012
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Phase-field models for brittle and cohesive fracture
Julien Vignollet, Stefan May, René De Borst, and Clemens V Verhoosel · 2014
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A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework
Michael J. Borden, Thomas J.R. Hughes, Chad M. Landis, and Clemens V. Verhoosel · 2014
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Phase field modeling of fracture in multi-physics problems. part i. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids
Christian Miehe, Lisa-Marie Schänzel, and Heike Ulmer · 2015
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Phase-field modeling of ductile fracture
M. Ambati, T. Gerasimov, and L. De Lorenzis · 2015
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Phase field modeling of fracture in multi-physics problems. part ii. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids
C. Miehe, M. Hofacker, L.-M. Schänzel, and F. Aldakheel · 2015
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A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
Timo Heister, Mary F. Wheeler, and Thomas Wick · 2015
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A numerical assessment of phase-field models for brittle and cohesive fracture:
Stefan May, Julien Vignollet, and Rene De Borst · 2015
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An assessment of the phase field formulation for crack growth
Markus Klinsmann, Daniele Rosato, Marc Kamlah, and Robert M McMeeking · 2015
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A review on phase-field models of brittle fracture and a new fast hybrid formulation
Marreddy Ambati, Tymofiy Gerasimov, and Laura De Lorenzis · 2015
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An adaptive multiscale phase field method for brittle fracture
RU Patil, BK Mishra, and IV Singh · 2018
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A non-intrusive global/local approach applied to phase-field modeling of brittle fracture
Tymofiy Gerasimov, Nima Noii, Olivier Allix, and Laura De Lorenzis · 2018
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A variational phase-field model for hydraulic fracturing in porous media
Chukwudi Chukwudozie, Blaise Bourdin, and Keita Yoshioka · 2019
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The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity
Lam H Nguyen and Dominik Schillinger · 2019
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On penalization in variational phase-field models of brittle fracture
Tymofiy Gerasimov and Laura De Lorenzis · 2019
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Phase-field modeling of hydraulic fracture
Zachary A. Wilson and Chad M. Landis · 2016
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A line search assisted monolithic approach for phase-field computing of brittle fracture
T. Gerasimov and L. De Lorenzis · 2016
Cited alongside, same era.
A fracture-controlled path-following technique for phase-field modeling of brittle fracture
N Singh, CV Verhoosel, R De Borst, and EH Van Brummelen · 2016
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Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization
C Miehe, S Teichtmeister, and F Aldakheel · 2016
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Goal functional evaluations for phase-field fracture using pu-based dwr mesh adaptivity
Thomas Wick · 2016
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A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects
Michael J Borden, Thomas JR Hughes, Chad M Landis, Amin Anvari, and Isaac J Lee · 2016
Cited alongside, same era.
Bézier extraction and adaptive refinement of truncated hierarchical nurbs
P Hennig, S Müller, and M Kästner · 2016
Cited alongside, same era.
Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition
Chintan Jansari, K Kannan, RK Annabattula, S Natarajan, et al · 2019
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Phase-field modeling of brittle fracture with multi-level hp-fem and the finite cell method
Sindhu Nagaraja, Mohamed Elhaddad, Marreddy Ambati, Stefan Kollmannsberger, Laura De Lorenzis, and Ernst Rank · 2019
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Adaptive phase field analysis with dual hierarchical meshes for brittle fracture
Somdatta Goswami, Cosmin Anitescu, and Timon Rabczuk · 2019
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A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking
Yousef Heider and WaiChing Sun · 2020
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A generalized phase field multiscale finite element method for brittle fracture
Savvas P Triantafyllou and Emmanouil G Kakouris · 2020
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An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture
Nima Noii, Fadi Aldakheel, Thomas Wick, and Peter Wriggers · 2020
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A phase field approach for damage propagation in periodic microstructured materials
Francesca Fantoni, Andrea Bacigalupo, Marco Paggi, and Josè Reinoso · 2020
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A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media
Bang He, Louis Schuler, and Pania Newell · 2020
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A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture
Alena Kopaničáková and Rolf Krause · 2020
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Adaptive fourth-order phase field analysis for brittle fracture
Somdatta Goswami, Cosmin Anitescu, and Timon Rabczuk · 2020
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Computational homogenisation of phase-field fracture
Ritukesh Bharali, Fredrik Larsson, and Ralf Jänicke · 2021
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Nucleation under multi-axial loading in variational phase-field models of brittle fracture
Laura De Lorenzis and Corrado Maurini · 2021
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Phase field modeling of fracture with isogeometric analysis and machine learning methods
Somdatta Goswami · 2021
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An accelerated staggered scheme for variational phase-field models of brittle fracture
Erlend Storvik, Jakub Wiktor Both, Juan Michael Sargado, Jan Martin Nordbotten, and Florin Adrian Radu · 2021
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