2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture

In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard. The method is based on the rate-independent variational principle of diffuse fracture. The phase-field is a scalar variable between 0 and 1 wh...

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Published in:	Finite elements in analysis and design Vol. 130; pp. 27 - 38
Main Authors:	Molnár, Gergely, Gravouil, Anthony
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.08.2017 Elsevier BV Elsevier
Subjects:	Abaqus UEL Brittle fracture Coalescing Computer simulation Crack propagation Cracks Engineering Sciences Finite element analysis Finite element method Fracture mechanics Mathematical models Mechanics Phase-field Robustness (mathematics) Solid mechanics Staggered solution Stiffness Three dimensional models Finite element method Phase-field Staggered solution Brittle fracture Abaqus UEL Crack propagation
ISSN:	0168-874X, 1872-6925
Online Access:	Get full text
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Abstract	In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard. The method is based on the rate-independent variational principle of diffuse fracture. The phase-field is a scalar variable between 0 and 1 which connects broken and unbroken regions. If its value reaches one the material is fully broken, thus both its stiffness and stress are reduced to zero. The elastic displacement and the fracture problem are decoupled and solved separately as a staggered solution. The approach does not need predefined cracks and it can simulate curvilinear fracture paths, branching and even crack coalescence. Several examples are provided to explain the advantages and disadvantages of the method. The provided source codes and the tutorials make it easy for practicing engineers and scientists to model diffuse crack propagation in a familiar computational environment. •Diffuse brittle crack propagation modeled with phase-field method.•Staggered, split scheme solution for elastic and phase-field problem.•Easy to use open source UEL implementation in Abaqus/Standard for practical purposes.
AbstractList	In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard. The method is based on the rate-independent variational principle of diffuse fracture. The phase-field is a scalar variable between 0 and 1 which connects broken and unbroken regions. If its value reaches one the material is fully broken, thus both its stiffness and stress are reduced to zero. The elastic displacement and the fracture problem are decoupled and solved separately as a staggered solution. The approach does not need predefined cracks and it can simulate curvilinear fracture paths, branching and even crack coalescence. Several examples are provided to explain the advantages and disadvantages of the method. The provided source codes and the tutorials make it easy for practicing engineers and scientists to model diffuse crack propagation in a familiar computational environment. In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard. The method is based on the rate-independent variational principle of diffuse fracture. The phase-field is a scalar variable between 0 and 1 which connects broken and unbroken regions. If its value reaches one the material is fully broken, thus both its stiffness and stress are reduced to zero. The elastic displacement and the fracture problem are decoupled and solved separately as a staggered solution. The approach does not need predefined cracks and it can simulate curvilinear fracture paths, branching and even crack coalescence. Several examples are provided to explain the advantages and disadvantages of the method. The provided source codes and the tutorials make it easy for practicing engineers and scientists to model diffuse crack propagation in a familiar computational environment. •Diffuse brittle crack propagation modeled with phase-field method.•Staggered, split scheme solution for elastic and phase-field problem.•Easy to use open source UEL implementation in Abaqus/Standard for practical purposes.
Author	Molnár, Gergely Gravouil, Anthony
Author_xml	– sequence: 1 givenname: Gergely surname: Molnár fullname: Molnár, Gergely email: gmolnar.work@gmail.com – sequence: 2 givenname: Anthony surname: Gravouil fullname: Gravouil, Anthony
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Cites_doi	10.1016/S0022-5096(98)00034-9 10.1016/S0966-9795(01)00008-5 10.1007/s002050100187 10.1016/j.jallcom.2006.08.336 10.1007/BF00020156 10.1038/nmat3115 10.1016/j.actamat.2014.12.016 10.1023/A:1007545213010 10.1016/j.finel.2015.12.005 10.1002/nme.429 10.1016/j.cma.2005.10.005 10.1016/j.actamat.2016.03.053 10.1098/rsta.1921.0006 10.1016/j.actamat.2016.05.027 10.1016/S0167-6636(97)00048-3 10.1016/j.cma.2010.04.011 10.1002/nme.4886 10.1016/j.commatsci.2014.05.071 10.1016/S0045-7949(97)00073-4 10.4028/www.scientific.net/AMM.182-183.1524 10.1002/nme.857 10.1016/j.jmps.2013.06.007 10.1002/nme.2861 10.1016/j.ijplas.2016.04.011 10.1007/978-3-662-43081-1_5 10.1016/j.cma.2014.11.017 10.1016/j.jnoncrysol.2016.02.024 10.1002/nme.3069 10.1002/nme.4387 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J 10.1002/cpa.3160420503 10.1016/j.cma.2014.11.016 10.1016/0013-7944(95)00247-2 10.1016/j.cma.2008.12.028 10.1016/S0022-5096(99)00028-9
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References	Francfort, Marigo (bib14) 1998; 46 Miehe, Schänzel (bib22) 2014; 65 Bourdin, Francfort, Marigo (bib11) 2008 Miehe, Welschinger, Hofacker (bib12) 2010; 83 Buliga (bib15) 1998; 52 Choe, Chen, Schneibel, Ritchie (bib30) 2001; 9 Bourdin, Francfort, Marigo (bib16) 2000; 48 Kermouche, Guillonneau, Michler, Teisseire, Barthel (bib4) 2016; 114 Ritchie (bib28) 2011; 10 Moës, Gravouil, Belytschko (bib9) 2002; 53 Gürses, Miehe (bib10) 2009; 198 ABAQUS, ABAQUS Documentation, Dassault Systemes, Providence, RI, USA, 2011. Molnár, Ferentzi, Weltsch, Szebényi, Borbás, Bojtár (bib38) 2016; 59 Miehe, Aldakheel, Raina (bib37) 2016; 84 Mumford, Shah (bib13) 1989; 42 Miehe, Hofacker, Schänzel, Aldakheel (bib25) 2015; 294 Msekh, Sargado, Jamshidian, Areias, Rabczuk (bib18) 2015; 96 Peng, Wang (bib5) 2012; 182–183 Singh, Verhoosel, de Borst, van Brummelen (bib23) 2016; 113 G.R. Irwin, Fracture, Springer Berlin Heidelberg, Berlin, Heidelberg, 1958, pp. 551–590. Zienkiewicz, Taylor, Fox (bib39) 2014 Cazes, Moës (bib34) 2015; 103 Miehe, Hofacker, Welschinger (bib20) 2010; 199 Moës, Stolz, Bernard, Chevaugeon (bib27) 2011; 86 Griffith (bib1) 1921; 221 Molnár, Ganster, Török, Tanguy (bib35) 2016; 440 Zhou, Molinari (bib6) 2004; 59 Moës, Dolbow, Belytschko (bib8) 1999; 46 Bittencourt, Wawrzynek, Ingraffea, Sousa (bib33) 1996; 55 Azevedo, Lemos (bib7) 2006; 195 Mueller, Pejchal, Žagar, Singh, Cantoni, Mortensen (bib36) 2015; 86 Melin (bib31) 1983; 23 Miehe (bib26) 1998; 66 Rountree, Prades, Bonamy, Bouchaud, Kalia, Guillot (bib29) 2007; 434–435 Miehe, Schänzel, Ulmer (bib24) 2015; 294 Dal Maso, Toader (bib17) 2002; 162 Molnár, Ganster, Tanguy, Barthel, Kermouche (bib3) 2016; 111 Hofacker, Miehe (bib21) 2013; 93 Sumi, Wang (bib32) 1998; 28 Bourdin (10.1016/j.finel.2017.03.002_bib16) 2000; 48 Peng (10.1016/j.finel.2017.03.002_bib5) 2012; 182–183 Choe (10.1016/j.finel.2017.03.002_bib30) 2001; 9 Singh (10.1016/j.finel.2017.03.002_bib23) 2016; 113 Ritchie (10.1016/j.finel.2017.03.002_bib28) 2011; 10 Miehe (10.1016/j.finel.2017.03.002_bib20) 2010; 199 Bittencourt (10.1016/j.finel.2017.03.002_bib33) 1996; 55 Miehe (10.1016/j.finel.2017.03.002_bib22) 2014; 65 Moës (10.1016/j.finel.2017.03.002_bib8) 1999; 46 Mueller (10.1016/j.finel.2017.03.002_bib36) 2015; 86 Msekh (10.1016/j.finel.2017.03.002_bib18) 2015; 96 Mumford (10.1016/j.finel.2017.03.002_bib13) 1989; 42 Miehe (10.1016/j.finel.2017.03.002_bib12) 2010; 83 Molnár (10.1016/j.finel.2017.03.002_bib38) 2016; 59 Francfort (10.1016/j.finel.2017.03.002_bib14) 1998; 46 Buliga (10.1016/j.finel.2017.03.002_bib15) 1998; 52 Miehe (10.1016/j.finel.2017.03.002_bib25) 2015; 294 Miehe (10.1016/j.finel.2017.03.002_bib37) 2016; 84 10.1016/j.finel.2017.03.002_bib19 Moës (10.1016/j.finel.2017.03.002_bib27) 2011; 86 Sumi (10.1016/j.finel.2017.03.002_bib32) 1998; 28 Hofacker (10.1016/j.finel.2017.03.002_bib21) 2013; 93 Griffith (10.1016/j.finel.2017.03.002_bib1) 1921; 221 Melin (10.1016/j.finel.2017.03.002_bib31) 1983; 23 Cazes (10.1016/j.finel.2017.03.002_bib34) 2015; 103 Dal Maso (10.1016/j.finel.2017.03.002_bib17) 2002; 162 Molnár (10.1016/j.finel.2017.03.002_bib35) 2016; 440 Rountree (10.1016/j.finel.2017.03.002_bib29) 2007; 434–435 Zienkiewicz (10.1016/j.finel.2017.03.002_bib39) 2014 Molnár (10.1016/j.finel.2017.03.002_bib3) 2016; 111 Azevedo (10.1016/j.finel.2017.03.002_bib7) 2006; 195 Gürses (10.1016/j.finel.2017.03.002_bib10) 2009; 198 Kermouche (10.1016/j.finel.2017.03.002_bib4) 2016; 114 Bourdin (10.1016/j.finel.2017.03.002_bib11) 2008 Miehe (10.1016/j.finel.2017.03.002_bib24) 2015; 294 Moës (10.1016/j.finel.2017.03.002_bib9) 2002; 53 Miehe (10.1016/j.finel.2017.03.002_bib26) 1998; 66 10.1016/j.finel.2017.03.002_bib2 Zhou (10.1016/j.finel.2017.03.002_bib6) 2004; 59
References_xml	– volume: 199 start-page: 2765 year: 2010 end-page: 2778 ident: bib20 article-title: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits publication-title: Comput. Methods Appl. Mech. Eng. – volume: 93 start-page: 276 year: 2013 end-page: 301 ident: bib21 article-title: A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns publication-title: Int. J. Numer. Methods Eng. – volume: 53 start-page: 2549 year: 2002 end-page: 2568 ident: bib9 article-title: Non-planar 3D crack growth by the extended finite element and level sets – Part I: mechanical model publication-title: Int. J. Numer. Methods Eng. – volume: 46 start-page: 1319 year: 1998 end-page: 1342 ident: bib14 article-title: Revisiting brittle fracture as an energy minimization problem publication-title: J. Mech. Phys. Solids – volume: 23 start-page: 37 year: 1983 end-page: 45 ident: bib31 article-title: Why do cracks avoid each other? publication-title: Int. J. Fract. – volume: 84 start-page: 1 year: 2016 end-page: 32 ident: bib37 article-title: Phase field modeling of ductile fracture at finite strains: a variational gradient-extended plasticity-damage theory publication-title: Int. J. Plast. – volume: 86 start-page: 358 year: 2011 end-page: 380 ident: bib27 article-title: A level set based model for damage growth: the thick level set approach publication-title: Int. J. Numer. Methods Eng. – volume: 195 start-page: 4579 year: 2006 end-page: 4593 ident: bib7 article-title: Hybrid discrete element/finite element method for fracture analysis publication-title: Comput. Methods Appl. Mech. Eng. – volume: 65 start-page: 93 year: 2014 end-page: 113 ident: bib22 article-title: Phase field modeling of fracture in rubbery polymers. Part I: finite elasticity coupled with brittle failure publication-title: J. Mech. Phys. Solids – volume: 66 start-page: 37 year: 1998 end-page: 43 ident: bib26 article-title: Comparison of two algorithms for the computation of fourth-order isotropic tensor functions publication-title: Comput. Struct. – volume: 46 start-page: 131 year: 1999 end-page: 150 ident: bib8 article-title: A finite element method for crack growth without remeshing publication-title: Int. J. Numer. Methods Eng. – volume: 103 start-page: 114 year: 2015 end-page: 143 ident: bib34 article-title: Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture publication-title: Int. J. Numer. Methods Eng. – volume: 111 start-page: 129 year: 2016 end-page: 137 ident: bib3 article-title: Densification dependent yield criteria for sodium silicate glasses – an atomistic simulation approach publication-title: Acta Mater. – volume: 42 start-page: 577 year: 1989 end-page: 685 ident: bib13 article-title: Optimal approximations by piecewise smooth functions and associated variational problems publication-title: Commun. Pure Appl. Math. – volume: 294 start-page: 486 year: 2015 end-page: 522 ident: bib25 article-title: 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 publication-title: Comput. Methods Appl. Mech. Eng. – volume: 86 start-page: 385 year: 2015 end-page: 395 ident: bib36 article-title: Fracture toughness testing of nanocrystalline alumina and fused quartz using chevron-notched microbeams publication-title: Acta Mater. – volume: 294 start-page: 449 year: 2015 end-page: 485 ident: bib24 article-title: 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 publication-title: Comput. Methods Appl. Mech. Eng. – volume: 113 start-page: 14 year: 2016 end-page: 29 ident: bib23 article-title: A fracture-controlled path-following technique for phase-field modeling of brittle fracture publication-title: Finite Elem. Anal. Des. – volume: 9 start-page: 319 year: 2001 end-page: 329 ident: bib30 article-title: Ambient to high temperature fracture toughness and fatigue-crack propagation behavior in a Mo–12Si–8.5B (at%) intermetallic publication-title: Intermetallics – volume: 440 start-page: 12 year: 2016 end-page: 25 ident: bib35 article-title: Sodium effect on static mechanical behavior of md-modeled sodium silicate glasses publication-title: J. Non-Cryst. Solids – volume: 10 start-page: 817 year: 2011 end-page: 822 ident: bib28 article-title: The conflicts between strength and toughness publication-title: Nat. Mater. – year: 2014 ident: bib39 article-title: The Finite Element Method for Solid and Structural Mechanics – volume: 59 start-page: 1 year: 2016 end-page: 10 ident: bib38 article-title: Fragmentation of wedge loaded tempered structural glass publication-title: Glass Struct. Eng. – volume: 83 start-page: 1273 year: 2010 end-page: 1311 ident: bib12 article-title: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations publication-title: Int. J. Numer. Methods Eng. – reference: ABAQUS, ABAQUS Documentation, Dassault Systemes, Providence, RI, USA, 2011. – volume: 182–183 start-page: 1524 year: 2012 end-page: 1528 ident: bib5 article-title: A node split method for crack growth problem publication-title: Appl. Mech. Mater. – volume: 114 start-page: 146 year: 2016 end-page: 153 ident: bib4 article-title: Perfectly plastic flow in silica glass publication-title: Acta Mater. – volume: 52 start-page: 201 year: 1998 ident: bib15 article-title: Energy minimizing brittle crack propagation publication-title: J. Elast. – volume: 28 start-page: 197 year: 1998 end-page: 206 ident: bib32 article-title: A finite-element simulation method for a system of growing cracks in a heterogeneous material publication-title: Mech. Mater. – volume: 198 start-page: 1413 year: 2009 end-page: 1428 ident: bib10 article-title: A computational framework of three-dimensional configurational-force-driven brittle crack propagation publication-title: Comput. Methods Appl. Mech. Eng. – volume: 55 start-page: 321 year: 1996 end-page: 334 ident: bib33 article-title: Quasi-automatic simulation of crack propagation for 2D LEFM problems publication-title: Eng. Fract. Mech. – year: 2008 ident: bib11 article-title: The Variational Approach to Fracture – volume: 221 start-page: 163 year: 1921 end-page: 198 ident: bib1 article-title: The phenomena of rupture and flow in solids publication-title: Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. – volume: 162 start-page: 101 year: 2002 end-page: 135 ident: bib17 article-title: A model for the quasi-static growth of brittle fractures: existence and approximation results publication-title: Arch. Ration. Mech. Anal. – volume: 59 start-page: 1 year: 2004 end-page: 24 ident: bib6 article-title: Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency publication-title: Int. J. Numer. Methods Eng. – volume: 48 start-page: 797 year: 2000 end-page: 826 ident: bib16 article-title: Numerical experiments in revisited brittle fracture publication-title: J. Mech. Phys. Solids – volume: 96 start-page: 472 year: 2015 end-page: 484 ident: bib18 article-title: Abaqus implementation of phase-field model for brittle fracture publication-title: Comput. Mater. Sci. – volume: 434–435 start-page: 60 year: 2007 end-page: 63 ident: bib29 article-title: A unified study of crack propagation in amorphous silica: using experiments and simulations publication-title: J. Alloy. Compd. – reference: G.R. Irwin, Fracture, Springer Berlin Heidelberg, Berlin, Heidelberg, 1958, pp. 551–590. – volume: 46 start-page: 1319 issue: 8 year: 1998 ident: 10.1016/j.finel.2017.03.002_bib14 article-title: Revisiting brittle fracture as an energy minimization problem publication-title: J. Mech. Phys. Solids doi: 10.1016/S0022-5096(98)00034-9 – volume: 9 start-page: 319 issue: 4 year: 2001 ident: 10.1016/j.finel.2017.03.002_bib30 article-title: Ambient to high temperature fracture toughness and fatigue-crack propagation behavior in a Mo–12Si–8.5B (at%) intermetallic publication-title: Intermetallics doi: 10.1016/S0966-9795(01)00008-5 – volume: 162 start-page: 101 issue: 2 year: 2002 ident: 10.1016/j.finel.2017.03.002_bib17 article-title: A model for the quasi-static growth of brittle fractures: existence and approximation results publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050100187 – volume: 434–435 start-page: 60 year: 2007 ident: 10.1016/j.finel.2017.03.002_bib29 article-title: A unified study of crack propagation in amorphous silica: using experiments and simulations publication-title: J. Alloy. Compd. doi: 10.1016/j.jallcom.2006.08.336 – volume: 23 start-page: 37 issue: 1 year: 1983 ident: 10.1016/j.finel.2017.03.002_bib31 article-title: Why do cracks avoid each other? publication-title: Int. J. Fract. doi: 10.1007/BF00020156 – volume: 59 start-page: 1 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib38 article-title: Fragmentation of wedge loaded tempered structural glass publication-title: Glass Struct. Eng. – volume: 10 start-page: 817 issue: 11 year: 2011 ident: 10.1016/j.finel.2017.03.002_bib28 article-title: The conflicts between strength and toughness publication-title: Nat. Mater. doi: 10.1038/nmat3115 – volume: 86 start-page: 385 year: 2015 ident: 10.1016/j.finel.2017.03.002_bib36 article-title: Fracture toughness testing of nanocrystalline alumina and fused quartz using chevron-notched microbeams publication-title: Acta Mater. doi: 10.1016/j.actamat.2014.12.016 – volume: 52 start-page: 201 issue: 3 year: 1998 ident: 10.1016/j.finel.2017.03.002_bib15 article-title: Energy minimizing brittle crack propagation publication-title: J. Elast. doi: 10.1023/A:1007545213010 – volume: 113 start-page: 14 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib23 article-title: A fracture-controlled path-following technique for phase-field modeling of brittle fracture publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2015.12.005 – volume: 53 start-page: 2549 issue: 11 year: 2002 ident: 10.1016/j.finel.2017.03.002_bib9 article-title: Non-planar 3D crack growth by the extended finite element and level sets – Part I: mechanical model publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.429 – volume: 195 start-page: 4579 issue: 33–36 year: 2006 ident: 10.1016/j.finel.2017.03.002_bib7 article-title: Hybrid discrete element/finite element method for fracture analysis publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2005.10.005 – volume: 111 start-page: 129 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib3 article-title: Densification dependent yield criteria for sodium silicate glasses – an atomistic simulation approach publication-title: Acta Mater. doi: 10.1016/j.actamat.2016.03.053 – year: 2008 ident: 10.1016/j.finel.2017.03.002_bib11 – ident: 10.1016/j.finel.2017.03.002_bib19 – volume: 221 start-page: 163 issue: 582–593 year: 1921 ident: 10.1016/j.finel.2017.03.002_bib1 article-title: The phenomena of rupture and flow in solids publication-title: Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. doi: 10.1098/rsta.1921.0006 – volume: 114 start-page: 146 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib4 article-title: Perfectly plastic flow in silica glass publication-title: Acta Mater. doi: 10.1016/j.actamat.2016.05.027 – volume: 28 start-page: 197 issue: 1–4 year: 1998 ident: 10.1016/j.finel.2017.03.002_bib32 article-title: A finite-element simulation method for a system of growing cracks in a heterogeneous material publication-title: Mech. Mater. doi: 10.1016/S0167-6636(97)00048-3 – volume: 199 start-page: 2765 issue: 45–48 year: 2010 ident: 10.1016/j.finel.2017.03.002_bib20 article-title: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2010.04.011 – year: 2014 ident: 10.1016/j.finel.2017.03.002_bib39 – volume: 103 start-page: 114 issue: 2 year: 2015 ident: 10.1016/j.finel.2017.03.002_bib34 article-title: Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.4886 – volume: 96 start-page: 472 issue: Part B year: 2015 ident: 10.1016/j.finel.2017.03.002_bib18 article-title: Abaqus implementation of phase-field model for brittle fracture publication-title: Comput. Mater. Sci. doi: 10.1016/j.commatsci.2014.05.071 – volume: 66 start-page: 37 issue: 1 year: 1998 ident: 10.1016/j.finel.2017.03.002_bib26 article-title: Comparison of two algorithms for the computation of fourth-order isotropic tensor functions publication-title: Comput. Struct. doi: 10.1016/S0045-7949(97)00073-4 – volume: 182–183 start-page: 1524 year: 2012 ident: 10.1016/j.finel.2017.03.002_bib5 article-title: A node split method for crack growth problem publication-title: Appl. Mech. Mater. doi: 10.4028/www.scientific.net/AMM.182-183.1524 – volume: 59 start-page: 1 issue: 1 year: 2004 ident: 10.1016/j.finel.2017.03.002_bib6 article-title: Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.857 – volume: 65 start-page: 93 year: 2014 ident: 10.1016/j.finel.2017.03.002_bib22 article-title: Phase field modeling of fracture in rubbery polymers. Part I: finite elasticity coupled with brittle failure publication-title: J. Mech. Phys. Solids doi: 10.1016/j.jmps.2013.06.007 – volume: 83 start-page: 1273 issue: 10 year: 2010 ident: 10.1016/j.finel.2017.03.002_bib12 article-title: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.2861 – volume: 84 start-page: 1 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib37 article-title: Phase field modeling of ductile fracture at finite strains: a variational gradient-extended plasticity-damage theory publication-title: Int. J. Plast. doi: 10.1016/j.ijplas.2016.04.011 – ident: 10.1016/j.finel.2017.03.002_bib2 doi: 10.1007/978-3-662-43081-1_5 – volume: 294 start-page: 486 year: 2015 ident: 10.1016/j.finel.2017.03.002_bib25 article-title: 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 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.11.017 – volume: 440 start-page: 12 year: 2016 ident: 10.1016/j.finel.2017.03.002_bib35 article-title: Sodium effect on static mechanical behavior of md-modeled sodium silicate glasses publication-title: J. Non-Cryst. Solids doi: 10.1016/j.jnoncrysol.2016.02.024 – volume: 86 start-page: 358 issue: 3 year: 2011 ident: 10.1016/j.finel.2017.03.002_bib27 article-title: A level set based model for damage growth: the thick level set approach publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.3069 – volume: 93 start-page: 276 issue: 3 year: 2013 ident: 10.1016/j.finel.2017.03.002_bib21 article-title: A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.4387 – volume: 46 start-page: 131 issue: 1 year: 1999 ident: 10.1016/j.finel.2017.03.002_bib8 article-title: A finite element method for crack growth without remeshing publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J – volume: 42 start-page: 577 issue: 5 year: 1989 ident: 10.1016/j.finel.2017.03.002_bib13 article-title: Optimal approximations by piecewise smooth functions and associated variational problems publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160420503 – volume: 294 start-page: 449 year: 2015 ident: 10.1016/j.finel.2017.03.002_bib24 article-title: 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 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.11.016 – volume: 55 start-page: 321 issue: 2 year: 1996 ident: 10.1016/j.finel.2017.03.002_bib33 article-title: Quasi-automatic simulation of crack propagation for 2D LEFM problems publication-title: Eng. Fract. Mech. doi: 10.1016/0013-7944(95)00247-2 – volume: 198 start-page: 1413 issue: 15–16 year: 2009 ident: 10.1016/j.finel.2017.03.002_bib10 article-title: A computational framework of three-dimensional configurational-force-driven brittle crack propagation publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2008.12.028 – volume: 48 start-page: 797 issue: 4 year: 2000 ident: 10.1016/j.finel.2017.03.002_bib16 article-title: Numerical experiments in revisited brittle fracture publication-title: J. Mech. Phys. Solids doi: 10.1016/S0022-5096(99)00028-9
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Snippet	In order to model brittle fracture, we have implemented a two and three dimensional phase-field method in the commercial finite element code Abaqus/Standard....
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SubjectTerms	Abaqus UEL Brittle fracture Coalescing Computer simulation Crack propagation Cracks Engineering Sciences Finite element analysis Finite element method Fracture mechanics Mathematical models Mechanics Phase-field Robustness (mathematics) Solid mechanics Staggered solution Stiffness Three dimensional models
Title	2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture
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