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2021 | OriginalPaper | Buchkapitel

16. Modeling Fracture in Straight Fiber and Tow-Steered Fiber Laminated Composites—A Phase Field Approach

verfasst von : Hirshikesh, Ratna Kumar Annabattula, Sundararajan Natarajan

Erschienen in: Recent Advances in Layered Materials and Structures

Verlag: Springer Singapore

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Abstract

The phase field approach for simulating fracture has gained significant attention in recent years due to the following salient features: (1) the scalar damage variable is implicitly used to describe the discontinuous surface; (2) the crack initiation and subsequent propagation and branching/coalescence are handled with minimal complexity and (3) can be integrated into any established traditional finite element software. The present work discusses the implementation aspects of the phase field method in an open source finite element package FEniCS for orthotropic materials and constant stiffness and tow-steered composite laminate. The main objectives of this work are: (a) studying the direction of crack propagation, and (b) investigating the fiber-matrix interface’s effect on the crack path. In particular, the emphasis is to explore the role played by the orientation of the fiber, initial crack location, and the inter-fiber spacing on the fracture pattern in the composite.

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Fußnoten
1
The phase-field models used by the mechanics community and further improvements will be discussed in Sect. 2 in detail.
 
Literatur
1.
Zurück zum Zitat Jones RM (1999) Mechanics of composite materials. Materials science & engineering series, 2nd edn. Taylor & Francis Jones RM (1999) Mechanics of composite materials. Materials science & engineering series, 2nd edn. Taylor & Francis
2.
Zurück zum Zitat Lugovy M, Orlovskaya N, Berroth K, Kuebler J (1999) Macrostructural engineering of ceramic-matrix layered composites. Compos Sci Technol 59(9):1429–1437CrossRef Lugovy M, Orlovskaya N, Berroth K, Kuebler J (1999) Macrostructural engineering of ceramic-matrix layered composites. Compos Sci Technol 59(9):1429–1437CrossRef
3.
Zurück zum Zitat Armstrong KB, Bevan LG, Cole WF (2005) Care and repair of advanced composites. Premiere Series Bks, SAE International Armstrong KB, Bevan LG, Cole WF (2005) Care and repair of advanced composites. Premiere Series Bks, SAE International
4.
Zurück zum Zitat Clegg WJ, Kendall K, Button TW, McN Alford N, Birchall JD, (1990) A simple way to make tough ceramics. Nature 347(6292):455–457 Clegg WJ, Kendall K, Button TW, McN Alford N, Birchall JD, (1990) A simple way to make tough ceramics. Nature 347(6292):455–457
5.
Zurück zum Zitat Zhang Y, Tang C, Zhang Y, Liang Z (2007) Fractural process and toughening mechanism of laminated ceramic composites. Acta Mechan Solida Sinica 20(2):141–148CrossRef Zhang Y, Tang C, Zhang Y, Liang Z (2007) Fractural process and toughening mechanism of laminated ceramic composites. Acta Mechan Solida Sinica 20(2):141–148CrossRef
6.
Zurück zum Zitat de Portu G, Micele L, Pezzotti G (2006) Laminated ceramic structures from oxide systems. Compos Part B Eng 37(6):556–567CrossRef de Portu G, Micele L, Pezzotti G (2006) Laminated ceramic structures from oxide systems. Compos Part B Eng 37(6):556–567CrossRef
7.
Zurück zum Zitat Tarlazzi A, Roncari E, Pinasco P, Guicciardi S, Melandri C, de Portu G (2000) Tribological behaviour of Al2O3/ZrO2-ZrO2 laminated composites. Wear 244(1):29–40CrossRef Tarlazzi A, Roncari E, Pinasco P, Guicciardi S, Melandri C, de Portu G (2000) Tribological behaviour of Al2O3/ZrO2-ZrO2 laminated composites. Wear 244(1):29–40CrossRef
8.
Zurück zum Zitat Lopes CS, Gürdal Z, Camanho PP (2008) Variable-stiffness composite panels: Buckling and first-ply failure improvements over straight-fibre laminates. Comput Struct 86(9):897–907CrossRef Lopes CS, Gürdal Z, Camanho PP (2008) Variable-stiffness composite panels: Buckling and first-ply failure improvements over straight-fibre laminates. Comput Struct 86(9):897–907CrossRef
9.
Zurück zum Zitat Hyer M, Charette R (1989) Use of curvilinear fiber format in composite structure design. In: AIAA/ASME/ASCE/AHS/ASC 30th structures, structural dynamics and materials conference, mobile, AL, pages 2137–2145 Hyer M, Charette R (1989) Use of curvilinear fiber format in composite structure design. In: AIAA/ASME/ASCE/AHS/ASC 30th structures, structural dynamics and materials conference, mobile, AL, pages 2137–2145
10.
Zurück zum Zitat Hyer M, Lee H (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos Struct 18:239–261CrossRef Hyer M, Lee H (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos Struct 18:239–261CrossRef
11.
Zurück zum Zitat Nagendra S, Kodiyalam S, Parthasarathy V (1995) Optimization of tow fiber paths for composite design. AIAA/ASME/ASCE/AHS/ASC 36th structures, structural dynamics and materials conference, New Orleans, pp 1031–1041 Nagendra S, Kodiyalam S, Parthasarathy V (1995) Optimization of tow fiber paths for composite design. AIAA/ASME/ASCE/AHS/ASC 36th structures, structural dynamics and materials conference, New Orleans, pp 1031–1041
12.
Zurück zum Zitat Carollo V, Reinoso J, Paggi M (2018) Modeling complex crack paths in ceramic laminates: a novel variational framework combining the phase field method of fracture and the cohesive zone model. J Eur Ceram Soc 38(8):2994–3003CrossRef Carollo V, Reinoso J, Paggi M (2018) Modeling complex crack paths in ceramic laminates: a novel variational framework combining the phase field method of fracture and the cohesive zone model. J Eur Ceram Soc 38(8):2994–3003CrossRef
13.
Zurück zum Zitat Margarita A, Eelco J, Hallett Stephen R, Paul W, Raimund R (2018) Analysis of skin-stringer debonding in composite panels through a two-way global-local method. Compos Struct 202:1280–1294CrossRef Margarita A, Eelco J, Hallett Stephen R, Paul W, Raimund R (2018) Analysis of skin-stringer debonding in composite panels through a two-way global-local method. Compos Struct 202:1280–1294CrossRef
14.
Zurück zum Zitat Wang BL, Sun YG, Zhang HY (2008) Multiple cracking of fiber/matrix composites-analysis of normal extension. Int J Solids Struct 45(14):4032–4048CrossRef Wang BL, Sun YG, Zhang HY (2008) Multiple cracking of fiber/matrix composites-analysis of normal extension. Int J Solids Struct 45(14):4032–4048CrossRef
15.
Zurück zum Zitat Greco F, Leonetti L, Lonetti P, Nevone Blasi P (2015) Crack propagation analysis in composite materials by using moving mesh and multiscale techniques. Comput Struct 153:201–216CrossRef Greco F, Leonetti L, Lonetti P, Nevone Blasi P (2015) Crack propagation analysis in composite materials by using moving mesh and multiscale techniques. Comput Struct 153:201–216CrossRef
16.
Zurück zum Zitat Maimì P, Camanho PP, Mayugo JA, Turon A (2011) Matrix cracking and delamination in laminated composites. Part I: ply constitutive law, first ply failure and onset of delamination. Mech Mater 43(4):169–185 Maimì P, Camanho PP, Mayugo JA, Turon A (2011) Matrix cracking and delamination in laminated composites. Part I: ply constitutive law, first ply failure and onset of delamination. Mech Mater 43(4):169–185
17.
Zurück zum Zitat Junya I, Shoichi N, Yoshitake I, Toshihiko K (2008) Fracture elongation of brittle/ductile multilayered steel composites with a strong interface. Scripta Mater 59(10):1055–1058CrossRef Junya I, Shoichi N, Yoshitake I, Toshihiko K (2008) Fracture elongation of brittle/ductile multilayered steel composites with a strong interface. Scripta Mater 59(10):1055–1058CrossRef
18.
Zurück zum Zitat Lacondemine T, Roux-Langlois C, Rouxel T (2017) Role of Poisson’s ratio mismatch on the crack path in glass matrix particulate composites. Int J Fract 207(1):73–85CrossRef Lacondemine T, Roux-Langlois C, Rouxel T (2017) Role of Poisson’s ratio mismatch on the crack path in glass matrix particulate composites. Int J Fract 207(1):73–85CrossRef
19.
Zurück zum Zitat Rebillat F, Lamon J, Guette A (2000) The concept of a strong interface applied to SiC/SiC composites with a BN interphase. Acta Mater 48(18):4609–4618CrossRef Rebillat F, Lamon J, Guette A (2000) The concept of a strong interface applied to SiC/SiC composites with a BN interphase. Acta Mater 48(18):4609–4618CrossRef
20.
Zurück zum Zitat Qingda Y, Brian C (2005) Cohesive models for damage evolution in laminated composites. Int J Fract 133:107–137CrossRef Qingda Y, Brian C (2005) Cohesive models for damage evolution in laminated composites. Int J Fract 133:107–137CrossRef
21.
Zurück zum Zitat Mohammadi S, Owen DRJ, Peric D (1998) A combined finite/discrete element algorithm for delamination analysis of composites. Finite Elements Anal Des 28:321–336CrossRef Mohammadi S, Owen DRJ, Peric D (1998) A combined finite/discrete element algorithm for delamination analysis of composites. Finite Elements Anal Des 28:321–336CrossRef
22.
Zurück zum Zitat XFEM simulation of delamination in composite laminates (2016) Compos Part Appl Sci Manuf 80:61–71 XFEM simulation of delamination in composite laminates (2016) Compos Part Appl Sci Manuf 80:61–71
23.
Zurück zum Zitat Cahill LMA, Natarajan S, Bordas SPA, O’Higgins RM, McCarthy CT (2013) An Experimental/Numerical investigation in to the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae. Compos Struct 107:119–130CrossRef Cahill LMA, Natarajan S, Bordas SPA, O’Higgins RM, McCarthy CT (2013) An Experimental/Numerical investigation in to the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae. Compos Struct 107:119–130CrossRef
24.
Zurück zum Zitat Adaptive discrete-smeared crack (A-DiSC) model for multi-scale progressive damage in composites. Compos Part Appl Sci Manuf 125:105513 Adaptive discrete-smeared crack (A-DiSC) model for multi-scale progressive damage in composites. Compos Part Appl Sci Manuf 125:105513
25.
Zurück zum Zitat Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mechan Phys Solids 46(8):1319–1342CrossRef Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mechan Phys Solids 46(8):1319–1342CrossRef
26.
Zurück zum Zitat Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mechan Phys Solids 48(4):797–826CrossRef Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mechan Phys Solids 48(4):797–826CrossRef
27.
Zurück zum Zitat Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. interfacial free energy. J Chem Phys 28(2):258–267 Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. interfacial free energy. J Chem Phys 28(2):258–267
28.
Zurück zum Zitat Chen LQ, Khachaturyan AG (1991) Computer simulation of structural transformations during precipitation of an ordered intermetallic phase. Acta Metall et Mater 39(11):2533–2551CrossRef Chen LQ, Khachaturyan AG (1991) Computer simulation of structural transformations during precipitation of an ordered intermetallic phase. Acta Metall et Mater 39(11):2533–2551CrossRef
29.
Zurück zum Zitat Galenko PK, Herlach DM, Funke O, Phanikumar G (2005) Phase-field modeling of dendritic solidification: verification for the model predictions with latest experimental data, chapter 7. Wiley, pp 52–60 Galenko PK, Herlach DM, Funke O, Phanikumar G (2005) Phase-field modeling of dendritic solidification: verification for the model predictions with latest experimental data, chapter 7. Wiley, pp 52–60
30.
Zurück zum Zitat Nele M, Bart B, Patrick W (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–294CrossRef Nele M, Bart B, Patrick W (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–294CrossRef
31.
Zurück zum Zitat Hohenberg PC, Krekhov AP (2015) An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns. Phys Rep 572:1–42CrossRef Hohenberg PC, Krekhov AP (2015) An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns. Phys Rep 572:1–42CrossRef
32.
Zurück zum Zitat Aronson I, Kalatsky VA, Vinokur VM (2000) Continuum field description of crack propagation. Phys Rev Lett 85(1):118–121, 7 Aronson I, Kalatsky VA, Vinokur VM (2000) Continuum field description of crack propagation. Phys Rev Lett 85(1):118–121, 7
33.
Zurück zum Zitat Karma A, Kessler DA, Levine H (2001) Phase-field model of mode III dynamic fracture. Phys Rev Lett 87(4):045501–1–045501–4 Karma A, Kessler DA, Levine H (2001) Phase-field model of mode III dynamic fracture. Phys Rev Lett 87(4):045501–1–045501–4
34.
Zurück zum Zitat Hervé H, Herbert L (2004) Dynamic instabilities of fracture under biaxial strain using a phase field model. Phys Rev Lett 93:105504CrossRef Hervé H, Herbert L (2004) Dynamic instabilities of fracture under biaxial strain using a phase field model. Phys Rev Lett 93:105504CrossRef
35.
Zurück zum Zitat Kuhn C, Müller R (2008) A phase field model for fracture. Proc Appl Math Mech 8(1):10223–10224CrossRef Kuhn C, Müller R (2008) A phase field model for fracture. Proc Appl Math Mech 8(1):10223–10224CrossRef
36.
Zurück zum Zitat Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77:3625–3634CrossRef Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77:3625–3634CrossRef
37.
Zurück zum Zitat Amor H, Jacques Marigo J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57(8):1209–1229CrossRef Amor H, Jacques Marigo J, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57(8):1209–1229CrossRef
38.
Zurück zum Zitat Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. Int J Numer Methods Eng 83:1273–1311CrossRef Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. Int J Numer Methods Eng 83:1273–1311CrossRef
39.
Zurück zum Zitat Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778CrossRef Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778CrossRef
40.
Zurück zum Zitat Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95CrossRef Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95CrossRef
41.
Zurück zum Zitat Marreddy A, Tymofiy G, Le Laura D (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55(2):383–405CrossRef Marreddy A, Tymofiy G, Le Laura D (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55(2):383–405CrossRef
42.
Zurück zum Zitat Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55(5):1017–1040CrossRef Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55(5):1017–1040CrossRef
43.
Zurück zum Zitat Schlüter A, Kuhn C, Müller R, Tomut M, Trautmann C, Weick H, Plate C (2017) Phase field modelling of dynamic thermal fracture in the context of irradiation damage. Continuum Mech Thermodyn 29(4):977–988CrossRef Schlüter A, Kuhn C, Müller R, Tomut M, Trautmann C, Weick H, Plate C (2017) Phase field modelling of dynamic thermal fracture in the context of irradiation damage. Continuum Mech Thermodyn 29(4):977–988CrossRef
44.
Zurück zum Zitat Hirshikesh, Natarajan S, Annabattula RK, Martínez-Pañeda E (2019) Phase field modelling of crack propagation in functionally graded materials. Compos Part Eng 169:239–248 Hirshikesh, Natarajan S, Annabattula RK, Martínez-Pañeda E (2019) Phase field modelling of crack propagation in functionally graded materials. Compos Part Eng 169:239–248
45.
Zurück zum Zitat Doan DH, Bui TQ, Duc ND, Fushinobu K (2016) Hybrid phase field simulation of dynamic crack propagation in functionally graded glass-filled epoxy. Compos Part Eng 99:266–276CrossRef Doan DH, Bui TQ, Duc ND, Fushinobu K (2016) Hybrid phase field simulation of dynamic crack propagation in functionally graded glass-filled epoxy. Compos Part Eng 99:266–276CrossRef
46.
Zurück zum Zitat Zhang P, Yao W, Hu X, Bui TQ (2020) 3D micromechanical progressive failure simulation for fiber-reinforced composites. Compos Struct, page 112534 Zhang P, Yao W, Hu X, Bui TQ (2020) 3D micromechanical progressive failure simulation for fiber-reinforced composites. Compos Struct, page 112534
47.
Zurück zum Zitat Hirshikesh, Natarajan S, Annabattula RK (2019) Modeling crack propagation in variable stiffness composite laminates using the phase field method. Compos Struct 209:424–433 Hirshikesh, Natarajan S, Annabattula RK (2019) Modeling crack propagation in variable stiffness composite laminates using the phase field method. Compos Struct 209:424–433
48.
Zurück zum Zitat Wilson ZA, Borden MJ, Landis CM (2013) A phase-field model for fracture in piezoelectric ceramics. Int J Fract 183(2):135–153CrossRef Wilson ZA, Borden MJ, Landis CM (2013) A phase-field model for fracture in piezoelectric ceramics. Int J Fract 183(2):135–153CrossRef
49.
Zurück zum Zitat Alex S, Ralf D, Erika T, Ola D (2020) Phase-field fracture modelling of crack nucleation and propagation in porous rock. Int J Fract 224(1):31–46CrossRef Alex S, Ralf D, Erika T, Ola D (2020) Phase-field fracture modelling of crack nucleation and propagation in porous rock. Int J Fract 224(1):31–46CrossRef
50.
Zurück zum Zitat Yin BB, Zhang LW (2019) Phase field method for simulating the brittle fracture of fiber reinforced composites. Eng Fract Mech 211:321–340CrossRef Yin BB, Zhang LW (2019) Phase field method for simulating the brittle fracture of fiber reinforced composites. Eng Fract Mech 211:321–340CrossRef
51.
Zurück zum Zitat Espadas-Escalante JJ, van Dijk NP, Isaksson P (2019) A phase-field model for strength and fracture analyses of fiber-reinforced composites. Compos Sci Technol 174:58–67CrossRef Espadas-Escalante JJ, van Dijk NP, Isaksson P (2019) A phase-field model for strength and fracture analyses of fiber-reinforced composites. Compos Sci Technol 174:58–67CrossRef
52.
Zurück zum Zitat Alessi R, Freddi F (2017) Phase-field modelling of failure in hybrid laminates. Compos Struct 181:9–25CrossRef Alessi R, Freddi F (2017) Phase-field modelling of failure in hybrid laminates. Compos Struct 181:9–25CrossRef
53.
Zurück zum Zitat Martínez-Pañeda E, Gallego R (2015) Numerical analysis of quasi-static fracture in functionally graded materials. Int J Mech Mater Des 11(4):405–424CrossRef Martínez-Pañeda E, Gallego R (2015) Numerical analysis of quasi-static fracture in functionally graded materials. Int J Mech Mater Des 11(4):405–424CrossRef
54.
Zurück zum Zitat Kristensen Philip K, Martínez-Pañeda E (2020) Phase field fracture modelling using quasi-newton methods and a new adaptive step scheme. Theoret Appl Fract Mech 107:102446CrossRef Kristensen Philip K, Martínez-Pañeda E (2020) Phase field fracture modelling using quasi-newton methods and a new adaptive step scheme. Theoret Appl Fract Mech 107:102446CrossRef
55.
Zurück zum Zitat Hirshikesh, Natarajan S, Annabattula RK (2019) A FEniCS implementation of the phase field method for quasi-static brittle fracture. Front Struct Civil Eng 13(2):380–396 Hirshikesh, Natarajan S, Annabattula RK (2019) A FEniCS implementation of the phase field method for quasi-static brittle fracture. Front Struct Civil Eng 13(2):380–396
56.
Zurück zum Zitat Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826CrossRef Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826CrossRef
57.
Zurück zum Zitat Wu J-Y, Nguyen V-P, Nguyen CT, Sutula D, Sinaie S, Bordas S (2019) Phase-field modeling of fracture. Advances in applied mechanics. Elsevier Wu J-Y, Nguyen V-P, Nguyen CT, Sutula D, Sinaie S, Bordas S (2019) Phase-field modeling of fracture. Advances in applied mechanics. Elsevier
58.
Zurück zum Zitat May S, Vignollet J, de Borst R (2015) A new arc-length control method based on the rates of the internal and the dissipated energy. Eng Comput 33(1):100–115CrossRef May S, Vignollet J, de Borst R (2015) A new arc-length control method based on the rates of the internal and the dissipated energy. Eng Comput 33(1):100–115CrossRef
59.
Zurück zum Zitat Gerasimov T, De Lorenzis L (2016) A line search assisted monolithic approach for phase-field computing of brittle fracture. Comput Methods Appl Mech Eng 312:276–303CrossRef Gerasimov T, De Lorenzis L (2016) A line search assisted monolithic approach for phase-field computing of brittle fracture. Comput Methods Appl Mech Eng 312:276–303CrossRef
60.
Zurück zum Zitat Blaise B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. Springer, Netherlands Blaise B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. Springer, Netherlands
61.
Zurück zum Zitat Fei Z, Weizhang H, Xianping L, Shicheng Z (2018) Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of newton’s iteration. J Comput Phys 356(1):127–149 Fei Z, Weizhang H, Xianping L, Shicheng Z (2018) Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of newton’s iteration. J Comput Phys 356(1):127–149
62.
Zurück zum Zitat Wu J-Y, Nguyen VP (2018) A length scale insensitive phase-field damage model for brittle fracture. J Mech Phys Solids 119:20–42CrossRef Wu J-Y, Nguyen VP (2018) A length scale insensitive phase-field damage model for brittle fracture. J Mech Phys Solids 119:20–42CrossRef
63.
Zurück zum Zitat Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118CrossRef Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118CrossRef
64.
Zurück zum Zitat Amiri F, Millán D, Arroyo M, Silani M, Rabczuk T (2016) Fourth order phase-field model for local max-ent approximants applied to crack propagation. Comput Methods Appl Mech Eng 312:254–275CrossRef Amiri F, Millán D, Arroyo M, Silani M, Rabczuk T (2016) Fourth order phase-field model for local max-ent approximants applied to crack propagation. Comput Methods Appl Mech Eng 312:254–275CrossRef
65.
Zurück zum Zitat Markus K, Daniele R, Marc K, McMeeking Robert M (2015) An assessment of the phase field formulation for crack growth. Comput Methods Appl Mech Eng 294:313–330CrossRef Markus K, Daniele R, Marc K, McMeeking Robert M (2015) An assessment of the phase field formulation for crack growth. Comput Methods Appl Mech Eng 294:313–330CrossRef
66.
Zurück zum Zitat Artina M, Fornasier M, Micheletti S, Perotto S (2015) Anisotropic mesh adaptation for crack detection in brittle materials. SIAM J Sci Comput 37(4):B633–B659CrossRef Artina M, Fornasier M, Micheletti S, Perotto S (2015) Anisotropic mesh adaptation for crack detection in brittle materials. SIAM J Sci Comput 37(4):B633–B659CrossRef
67.
Zurück zum Zitat Hirshikesh, Jansari C, Kannan K, Annabattula RK, Natarajan S (2019) Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition. Eng Fract Mech 220:106599 Hirshikesh, Jansari C, Kannan K, Annabattula RK, Natarajan S (2019) Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition. Eng Fract Mech 220:106599
68.
Zurück zum Zitat Xue Z, Sloan Scott W, Chet V, Daichao S (2017) A modification of the phase-field model for mixed mode crack propagation in rock-like materials. Comput Methods Appl Mech Eng 322:123–136CrossRef Xue Z, Sloan Scott W, Chet V, Daichao S (2017) A modification of the phase-field model for mixed mode crack propagation in rock-like materials. Comput Methods Appl Mech Eng 322:123–136CrossRef
69.
Zurück zum Zitat Shuwei Z, Xiaoying Z, Timon R (2019) Phase field modeling of brittle compressive-shear fractures in rock-like materials: a new driving force and a hybrid formulation. Comput Methods Appl Mech Eng 355:729–752CrossRef Shuwei Z, Xiaoying Z, Timon R (2019) Phase field modeling of brittle compressive-shear fractures in rock-like materials: a new driving force and a hybrid formulation. Comput Methods Appl Mech Eng 355:729–752CrossRef
70.
Zurück zum Zitat Abdulrazzak Msekh M (2017) Phase field modeling for fracture with applications to homogeneous and heterogeneous materials. Phd thesis, Bauhaus-Universität Weimar Abdulrazzak Msekh M (2017) Phase field modeling for fracture with applications to homogeneous and heterogeneous materials. Phd thesis, Bauhaus-Universität Weimar
71.
Zurück zum Zitat Felger J, Stein N, Becker W (2017) Mixed-mode fracture in open-hole composite plates of finite-width: an asymptotic coupled stress and energy approach. Int J Solids Struct 122–123:14–24CrossRef Felger J, Stein N, Becker W (2017) Mixed-mode fracture in open-hole composite plates of finite-width: an asymptotic coupled stress and energy approach. Int J Solids Struct 122–123:14–24CrossRef
72.
Zurück zum Zitat Zhang P, Hu X, Bui TQ, Yao W (2019) Phase field modeling of fracture in fiber reinforced composite laminate. Int J Mech Sci 161–162:105008CrossRef Zhang P, Hu X, Bui TQ, Yao W (2019) Phase field modeling of fracture in fiber reinforced composite laminate. Int J Mech Sci 161–162:105008CrossRef
73.
Zurück zum Zitat Yazdani S, Rust W, Wriggers P (2016) Delamination growth in composite laminates of variable stiffness. Int J Numer Methods Eng 108:1406–1424CrossRef Yazdani S, Rust W, Wriggers P (2016) Delamination growth in composite laminates of variable stiffness. Int J Numer Methods Eng 108:1406–1424CrossRef
74.
Zurück zum Zitat Wu Z, Weaver PM, Raju G, Kim BC (2012) Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Struct 60:163–172CrossRef Wu Z, Weaver PM, Raju G, Kim BC (2012) Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Struct 60:163–172CrossRef
75.
Zurück zum Zitat Wu Z, Raju G, Weaver Paul M (2013) Post-buckling analysis of variable angle tow composite plates. Int J Solids Struct 50(10):1770–1780CrossRef Wu Z, Raju G, Weaver Paul M (2013) Post-buckling analysis of variable angle tow composite plates. Int J Solids Struct 50(10):1770–1780CrossRef
76.
Zurück zum Zitat Ramesh K, Gupta S, Kelkar AA (1997) Evaluation of stress field parameters in fracture mechanics by photoelasticity–Revisited. Eng Fract Mech 56(1):25–45CrossRef Ramesh K, Gupta S, Kelkar AA (1997) Evaluation of stress field parameters in fracture mechanics by photoelasticity–Revisited. Eng Fract Mech 56(1):25–45CrossRef
Metadaten
Titel
Modeling Fracture in Straight Fiber and Tow-Steered Fiber Laminated Composites—A Phase Field Approach
verfasst von
Hirshikesh
Ratna Kumar Annabattula
Sundararajan Natarajan
Copyright-Jahr
2021
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-33-4550-8_16

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