Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

Tran Quoc THAI, Timon RABCZUK, Xiaoying ZHUANG

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Front. Struct. Civ. Eng. ›› 2020, Vol. 14 ›› Issue (2) : 267-279. DOI: 10.1007/s11709-019-0567-x
RESEARCH ARTICLE

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

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Abstract

We present a cohesive zone model for delamination in thin shells and composite structures. The isogeometric (IGA) thin shell model is based on Kirchhoff-Love theory. Non-Uniform Rational B-Splines (NURBS) are used to discretize the exact mid-surface of the shell geometry exploiting their C1-continuity property which avoids rotational degrees of freedom. The fracture process zone is modeled by interface elements with a cohesive law. Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.

Keywords

cohesive zone model / IGA / Kirchhoff-Love model / thin shell analysis / delamination

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Tran Quoc THAI, Timon RABCZUK, Xiaoying ZHUANG. Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model. Front. Struct. Civ. Eng., 2020, 14(2): 267‒279 https://doi.org/10.1007/s11709-019-0567-x

References

[1]
Rabczuk T. Computational methods for fracture in brittle and quasibrittle solids: State-of-the-art review and future perspectives. ISRN Applied Mathematics, 2013, 2013: 849231
[2]
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620
CrossRef Google scholar
[3]
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150
CrossRef Google scholar
[4]
Belytschko T, Gracie R, Ventura G. A review of extended/generalized finite element methods for material modeling. Modelling and Simulation in Materials Science and Engineering, 2009, 17(4): 043001
CrossRef Google scholar
[5]
Strouboulis T, Copps K, Babuška I. The generalized finite element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190(32–33): 4081–4193
CrossRef Google scholar
[6]
Belytschko T, Lu Y Y, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256
CrossRef Google scholar
[7]
Zhuang X, Augarde C, Mathisen K. Fracture modeling using meshless methods and level sets in 3d: Framework and modeling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998
CrossRef Google scholar
[8]
Zhuang X, Zhu H, Augarde C. An improved meshless shepard and least squares method possessing the delta property and requiring no singular weight function. Computational Mechanics, 2014, 53(2): 343–357
CrossRef Google scholar
[9]
Zhuang X, Augarde C, Bordas S. Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2d modelling. International Journal for Numerical Methods in Engineering, 2011, 86(2): 249–268
CrossRef Google scholar
[10]
Simo J C, Oliver J, Armero F. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Computational Mechanics, 1993, 12(5): 277–296
CrossRef Google scholar
[11]
Zhang Y, Zhuang X. Cracking elements: A self-propagating strong discontinuity embedded approach for quasi-brittle fracture. Finite Elements in Analysis and Design, 2018, 144: 84–100
CrossRef Google scholar
[12]
Zhang Y, Lackner R, Zeiml M, Mang H A. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 335–366
CrossRef Google scholar
[13]
Nikolić M, Do X N, Ibrahimbegovic A, Nikolić Ž. Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 480–499
CrossRef Google scholar
[14]
Nikolic M, Ibrahimbegovic A, Miscevic P. Brittle and ductile failure of rocks: Embedded discontinuity approach for representing mode I and mode II failure mechanisms. International Journal for Numerical Methods in Engineering, 2015, 102(8): 1507–1526
CrossRef Google scholar
[15]
Han F, Lubineau G, Azdoud Y, Askari A. A morphing approach to couple state-based peridynamics with classical continuum mechanics. Computer Methods in Applied Mechanics and Engineering, 2016, 301: 336–358
CrossRef Google scholar
[16]
Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
CrossRef Google scholar
[17]
Rabczuk T, Ren H. A peridynamics formulation for quasi-static fracture and contact in rock. Engineering Geology, 2017, 225: 42–48
CrossRef Google scholar
[18]
Hillerborg A, Modéer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773–781
CrossRef Google scholar
[19]
Schellekens J, De Borst R. A non-linear finite element approach for the analysis of mode-I free edge delamination in composites. International Journal of Solids and Structures, 1993, 30(9): 1239–1253
CrossRef Google scholar
[20]
Allix O, Ladeveze P, Corigliano A. Damage analysis of interlaminar fracture specimens. Composite Structures, 1995, 31(1): 61–74
CrossRef Google scholar
[21]
Alfano G, Crisfield M. Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues. International Journal for Numerical Methods in Engineering, 2001, 50(7): 1701–1736
CrossRef Google scholar
[22]
Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics, 1987, 54(3): 525–531
CrossRef Google scholar
[23]
Tvergaard V. Effect of fibre debonding in a whisker-reinforced metal. Materials Science and Engineering A, 1990, 125(2): 203–213
CrossRef Google scholar
[24]
Harper P W, Hallett S R. Cohesive zone length in numerical simulations of composite delamination. Engineering Fracture Mechanics, 2008, 75(16): 4774–4792
CrossRef Google scholar
[25]
Camanho P P, Davila C G, De Moura M. Numerical simulation of mixed-mode progressive delamination in composite materials. Journal of Composite Materials, 2003, 37(16): 1415–1438
CrossRef Google scholar
[26]
Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering, 1999, 44(9): 1267–1282
CrossRef Google scholar
[27]
Hohberg J M. A note on spurious oscillations in FEM joint elements. Earthquake Engineering & Structural Dynamics, 1990, 19(5): 773–779
CrossRef Google scholar
[28]
Nguyen V P, Kerfriden P, Bordas S P. Two- and three-dimensional isogeometric cohesive elements for composite delamination analysis. Composites. Part B, Engineering, 2014, 60: 193–212
CrossRef Google scholar
[29]
Sprenger W, Gruttmann F, Wagner W. Delamination growth analysis in laminated structures with continuum-based 3d-shell elements and a viscoplastic softening model. Computer Methods in Applied Mechanics and Engineering, 2000, 185(2–4): 123–139
CrossRef Google scholar
[30]
Borst R, Gutiérrez M A, Wells G N, Remmers J J, Askes H. Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis. International Journal for Numerical Methods in Engineering, 2004, 60(1): 289–315
CrossRef Google scholar
[31]
Sacco E, Lebon F. A damage-friction interface model derived from micromechanical approach. International Journal of Solids and Structures, 2012, 49(26): 3666–3680
CrossRef Google scholar
[32]
Freddi F, Sacco E. An interface damage model accounting for in plane effects. International Journal of Solids and Structures, 2014, 51(25–26): 4230–4244
CrossRef Google scholar
[33]
Simo J. On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 56-DOF finite element formulations. Computer Methods in Applied Mechanics and Engineering, 1993, 108(3–4): 319–339
CrossRef Google scholar
[34]
Simo J C, Fox D D, Rifai M S. On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory. Computer Methods in Applied Mechanics and Engineering, 1990, 79(1): 21–70
CrossRef Google scholar
[35]
Dolbow J, Moës N, Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36(3–4): 235–260
CrossRef Google scholar
[36]
Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411
CrossRef Google scholar
[37]
Asadpoure A, Mohammadi S. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. International Journal for Numerical Methods in Engineering, 2007, 69(10): 2150–2172
CrossRef Google scholar
[38]
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620
CrossRef Google scholar
[39]
Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69(7): 813–833
CrossRef Google scholar
[40]
Song J H, Areias P M, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868–893
CrossRef Google scholar
[41]
Meer F P, Sluys L J. A phantom node formulation with mixed mode cohesive law for splitting in laminates. International Journal of Fracture, 2009, 158(2): 107–124
CrossRef Google scholar
[42]
Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122
CrossRef Google scholar
[43]
Areias P, Rabczuk T, Camanho P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947
CrossRef Google scholar
[44]
Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350
CrossRef Google scholar
[45]
Thai T Q, Rabczuk T, Bazilevs Y, Meschke G. A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604
CrossRef Google scholar
[46]
Ambati M, De Lorenzis L. Phase-field modeling of brittle and ductile fracture in shells with isogeometric nurbs-based solid-shell elements. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 351–373
CrossRef Google scholar
[47]
Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192
CrossRef Google scholar
[48]
Wu J Y. Robust numerical implementation of non-standard phase-field damage models for failure in solids. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 767–797
CrossRef Google scholar
[49]
Wu J Y, Nguyen V P. A length scale insensitive phase-field damage model for brittle fracture. Journal of the Mechanics and Physics of Solids, 2018, 119: 20–42
CrossRef Google scholar
[50]
Rabczuk T, Areias P, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548
CrossRef Google scholar
[51]
Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109
CrossRef Google scholar
[52]
Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
[53]
Amiri F, Millán D, Arroyo M, Silani M, Rabczuk T. Fourth order phase-field model for local max-ent approximants applied to crack propagation. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 254–275
CrossRef Google scholar
[54]
Hughes T J, Cottrell J A, Bazilevs Y. Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39–41): 4135–4195
CrossRef Google scholar
[55]
Benson D, Bazilevs Y, Hsu M C, Hughes T. Isogeometric shell analysis: The Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering, 2010, 199(5–8): 276–289
CrossRef Google scholar
[56]
Benson D, Hartmann S, Bazilevs Y, Hsu M C, Hughes T. Blended isogeometric shells. Computer Methods in Applied Mechanics and Engineering, 2013, 255: 133–146
CrossRef Google scholar
[57]
Hosseini S, Remmers J J, Verhoosel C V, De Borst R. Propagation of delamination in composite materials with isogeometric continuum shell elements. International Journal for Numerical Methods in Engineering, 2015, 102(3–4): 159–179
CrossRef Google scholar
[58]
Bouclier R, Elguedj T, Combescure A. Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and B-method. Computer Methods in Applied Mechanics and Engineering, 2013, 267: 86–110
CrossRef Google scholar
[59]
Benson D, Bazilevs Y, Hsu M C, Hughes T. A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering, 2011, 200(13–16): 1367–1378
CrossRef Google scholar
[60]
Kiendl J, Bletzinger K U, Linhard J, Wüchner R. Isogeometric shell analysis with Kirchhoff-Love elements. Computer Methods in Applied Mechanics and Engineering, 2009, 198(49–52): 3902–3914
CrossRef Google scholar
[61]
Nguyen-Thanh N, Valizadeh N, Nguyen M, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291
CrossRef Google scholar
[62]
Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178
CrossRef Google scholar
[63]
Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger K U, Bazilevs Y, Rabczuk T. Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424
CrossRef Google scholar
[64]
Wang P, Xu J, Deng J, Chen F. Adaptive isogeometric analysis using rational PHT-splines. Computer Aided Design, 2011, 43(11): 1438–1448
CrossRef Google scholar
[65]
Reinoso J, Paggi M, Blázquez A. A nonlinear finite thickness cohesive interface element for modeling delamination in fibre-reinforced composite laminates. Composites. Part B, Engineering, 2017, 109: 116–128
CrossRef Google scholar
[66]
Verhoosel C V, Remmers J J, Gutiérrez M A. A dissipation-based arc-length method for robust simulation of brittle and ductile failure. International Journal for Numerical Methods in Engineering, 2009, 77(9): 1290–1321
CrossRef Google scholar
[67]
Kaliakin V, Li J. Insight into deficiencies associated with commonly used zero-thickness interface elements. Computers and Geotechnics, 1995, 17(2): 225–252
CrossRef Google scholar
[68]
Vignollet J, May S, de Borst R. On the numerical integration of isogeometric interface elements. International Journal for Numerical Methods in Engineering, 2015, 102(11): 1733–1749
CrossRef Google scholar
[69]
ASTM D5528-13. Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. ASTM International, 2013
[70]
Remmers J J C, Borst R, Verhoosel C V, Needleman A. The cohesive band model: A cohesive surface formulation with stress triaxiality. International Journal of Fracture, 2013, 181(2): 177–188
CrossRef Google scholar
[71]
Benzeggagh M L, Kenane M. Measurement of mixed-mode de lamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Science and Technology, 1996, 56(4): 439–449
CrossRef Google scholar

Acknowledgement

The authors would like to acknowledge the financial support from the Sofja Kovalevskaja Prize of the Alexander von Humboldt Foundation (Germany).

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2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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