Computational Mechanics

, Volume 62, Issue 3, pp 587–601 | Cite as

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff–Love shells. Part II: impact modeling

  • M. S. Pigazzini
  • Y. BazilevsEmail author
  • A. Ellison
  • H. Kim
Original Paper


In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff–Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff–Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff–Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.


Composite laminates Kirchhoff–Love shells Isogeometric analysis (IGA) NURBS Cohesive interface Impact damage 



This work was supported by NASA Advanced Composites Project No. 15-ACP1-0021. We thank F. Leone, C, Rose, and C. Davila from NASA Langley Research Center for their valuable comments and suggestions.


  1. 1.
    Choi H, Downs R, Chang F-K (1991) A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: part I-experiments. J Compos Mater 25:992–1011CrossRefGoogle Scholar
  2. 2.
    Richardson M, Wisheart M (1996) Review of low-velocity impact properties of composite materials. Compos A 27A:1123–1131CrossRefGoogle Scholar
  3. 3.
    Choi H, Chang F-K (1992) A model for predicting damage in graphite/epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 26:2134–2169CrossRefGoogle Scholar
  4. 4.
    Allix O, Ladevéze P (1992) Interlaminar interface modelling for the prediction of delamination. Compos Struct 22:235–242CrossRefGoogle Scholar
  5. 5.
    Allix O, Ladevéze P, Corigliano A (1995) Damage analysis of interlaminar fracture specimens. Compos Struct 31:61–74CrossRefGoogle Scholar
  6. 6.
    Mi Y, Crisfield A, Davies G (1998) Progressive delamination using interface elements. J Compos Mater 32:1246–1272CrossRefGoogle Scholar
  7. 7.
    Dàvila C, Camanho P, Turon A (2007) Cohesive elements for shells. Technical report 214869. NASA Langley Research CenterGoogle Scholar
  8. 8.
    Camanho P, Dàvila C, de Moura F (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Compos Mater 37:1415–1438CrossRefGoogle Scholar
  9. 9.
    Yang Q, Cox B (2005) Cohesive models for damage evolution in laminated composites. Int J Fract 133:107–137CrossRefzbMATHGoogle Scholar
  10. 10.
    Turon A, Camanho P, Costa J, Dàvila C (2006) A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech Mater 38:1072–1089CrossRefGoogle Scholar
  11. 11.
    Turon A, Camanho P, Costa J, Renart J (2010) Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: definition of interlaminar strengths and elastic stiffness. Compos Struct 92:1857–1864CrossRefGoogle Scholar
  12. 12.
    Ladevéze P, Dantec EL (1992) Damage modelling of the elementary ply for laminated composites. Compos Sci Technol 43:257–267CrossRefGoogle Scholar
  13. 13.
    Matzenmiller A, Lubliner J, Taylor R (1995) A constitutive model for anisotropic damage in fiber-composites. Mech Mater 20:125–152CrossRefGoogle Scholar
  14. 14.
    Dàvila C, Camanho P (2003) Failure criteria for FRP laminates in plane stress. Technical report NASA/TM-2003-212663. Langley Research Center, HamptonGoogle Scholar
  15. 15.
    Pinho S, Iannucci L, Robinson P (2006) Physically-based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking: part I: development. Compos A 37:63–73CrossRefGoogle Scholar
  16. 16.
    Pinho S, Iannucci L, Robinson P (2006) Physically-based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking: part II: FE implementation. Compos A 37:766–777CrossRefGoogle Scholar
  17. 17.
    Donadon M, Iannucci L, Falzon B, Hodgkinson J, de Almeida S (2008) A progressive failure model for composite laminates subjected to low velocity impact damage. Comput Struct 86:1232–1252CrossRefGoogle Scholar
  18. 18.
    Bouvet C, Rivallant S, Barrau J (2012) Low velocity impact modeling in composite laminates capturing permanent indentation. Compos Sci Technol 72:1977–1988CrossRefGoogle Scholar
  19. 19.
    Tan W, Falzon B, Chiu L, Price M (2015) Predicting low velocity impact damage and compression-after-impact (CAI) behaviour of composite laminates. Compos A 71:212–226CrossRefGoogle Scholar
  20. 20.
    Zhang Y, Zhu P, Lai X (2006) Finite element analysis of low-velocity impact damage in composite laminated plates. Mater Des 27:513–519CrossRefGoogle Scholar
  21. 21.
    Guan Z, Yang C (2002) Low-velocity impact and damage process of composite laminates. J Compos Mater 36:851–871CrossRefGoogle Scholar
  22. 22.
    Faggiani A, Falzon B (2010) Predicting low-velocity impact damage on a stiffened composite panel. Compos A 41:737–749CrossRefGoogle Scholar
  23. 23.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, LondonCrossRefzbMATHGoogle Scholar
  25. 25.
    Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Deng X, Korobenko A, Yan J, Bazilevs Y (2015) Isogeometric analysis of continuum damage in rotation-free composite shells. Comput Methods Appl Mech Eng 284:349–372MathSciNetCrossRefGoogle Scholar
  28. 28.
    Hsu M-C, Wang C, Herrema AJ, Schillinger D, Ghoshal A, Bazilevs Y (2015) An interactive geometry modeling and parametric design platform for isogeometric analysis. Comput Math Appl 70:1481–1500MathSciNetCrossRefGoogle Scholar
  29. 29.
    Hosseini S, Remmers J, Verhoosel C, de Borst R (2013) An isogeometric solid-like shell element for non-linear analysis. Int J Numer Meth Eng 95:238–256CrossRefzbMATHGoogle Scholar
  30. 30.
    Hosseini S, Remmers J, Verhoosel C, de Borst R (2014) An isogeometric continuum shell element for non-linear analysis. Comput Methods Appl Mech Eng 271:1–22MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Wriggers P (1995) Finite element algorithms for contact problems. Arch Comput Methods Eng 2:1–49MathSciNetCrossRefGoogle Scholar
  32. 32.
    Temizer I, Wriggers P, Hughes T (2012) Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with nurbs. Comput Methods Appl Mech Eng 209:115–128MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053MathSciNetCrossRefGoogle Scholar
  34. 34.
    Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–75MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    ABAQUS (2016) User’s manual. Providence, p 2016Google Scholar
  37. 37.
    Rivallant S, Bouvet C, Hongkarnjanakul N (2013) Failure analysis of CFRP laminates subjected to compression after impact: fe simulation using discrete interface elements. Compos A 55:83–93CrossRefGoogle Scholar
  38. 38.
    Hongkarnjanakul N, Bouvet C, Rivallant S (2013) Validation of low velocity impact modelling on different stacking sequences of CFRP laminates and influence of fibre failure. Compos Struct 106:549–559CrossRefGoogle Scholar
  39. 39.
    Bažant Z, Oh B (1983) Crack band theory for fracture of concrete. Mater Struct 16:155–177Google Scholar
  40. 40.
    Turon A, Dàvila C, Camanho P, Costa J (2007) An engineering solution for mesh size effects in the simulation of selamination using cohesive zone models. Eng Fract Mech 74:1665–1682CrossRefGoogle Scholar
  41. 41.
    Falk M, Needleman A, Rice J (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys IV 11:43–50Google Scholar
  42. 42.
    Yang Q, Cox B (2006) Fracture length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27:2095–2113CrossRefGoogle Scholar
  43. 43.
    Harper P, Hallett S (2008) Cohesive zone length in numerical simulations of composite delamination. Eng Fract Mech 75:4774–4792CrossRefGoogle Scholar
  44. 44.
    Xie J, Waas A, Rassaian M (2016) Estimating the process zone length of fracture tests used in characterizing composites. Int J Solids Struct 100–101:111–126CrossRefGoogle Scholar
  45. 45.
    Rose C, Dàvila C, Leone F Jr (2013) Analysis methods for progressive damage of composite structures. Technical Report 218024. NASA Langley Research CenterGoogle Scholar
  46. 46.
    Leone F Jr (2015) Deformation gradient tensor decomposition for representing matrix cracks in fiber-reinforced materials. Compos A 76:334–341CrossRefGoogle Scholar
  47. 47.
    Benson D, Bazilevs Y, Hsu M-C, Hughes T (2010) Isogeometric shell analysis: the Reissner–Mindlin shell. Comput Methods Appl Mech Eng 199:276–289MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Benson D, Bazilevs Y, Hsu M-C, Hughes T (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200:1367–1378MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Pijaudier-Cabot G, Bazant ZP (1987) Nonlocal damage theory. J Eng Mech 113:1512–1533CrossRefzbMATHGoogle Scholar
  50. 50.
    Bazant ZP, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. J Appl Mech 55:287–293CrossRefzbMATHGoogle Scholar
  51. 51.
    de Borst R, Pamin J, Peerlings RHJ, Sluys LJ (1995) Strain-based transient-gradient damage model for failure analyses. Comput Mech 17:130–141CrossRefzbMATHGoogle Scholar
  52. 52.
    Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based transient-gradient damage model for failure analyses. Comput Methods Appl Mech Eng 160:133–153CrossRefzbMATHGoogle Scholar
  53. 53.
    Hosseini S, Remmers JJC, de Borst R (2014) The incorporation of gradient damage models in shell elements. Int J Numer Meth Eng 98:391–398MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • M. S. Pigazzini
    • 1
  • Y. Bazilevs
    • 1
    Email author
  • A. Ellison
    • 1
  • H. Kim
    • 1
  1. 1.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA

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