, Volume 49, Issue 11, pp 2571–2586 | Cite as

The compressive behaviour of composites including fiber kinking: modelling across the scales

  • Olivier Allix
  • Nicolas Feld
  • Emmanuel Baranger
  • Jean-Mathieu Guimard
  • Cuong Ha-Minh
Multi-Scale and Multi-Physics Modelling for Complex Materials


A multiscale strategy is proposed for the simulation of compressive failure by kinking in laminated samples. The model is based on an hybrid description of the material: the composite is seen as an assembly of elementary cells made of homogenized fiber–matrix material and interfaces that are used as potential minimum cracking surfaces to explicitly represent discrete phenomena like splitting and localized delamination. The enrichment proposed in this study concerns the response of the elementary cells in compression/tension and shear. A nonlinear constitutive model inherited from a microscopic kinking theory and parametrized by the statistical fiber waviness is implemented. The average kink-band width defines the cells width, as a characteristic length of the model. Simulations of small structural samples are then performed with this model to illustrate its capabilities, the influence of boundary conditions and statistical fiber waviness, and the natural interactions between kinking and other degradation mechanisms.


Multiscale Modelling Failure Fragmentation Kinking Laminates 



This work has been partially carried out in the framework of the ANR (Agence Nationale de la Recherche) VulComp Phase 1 project, under the grants ANR-2006-MAPR-0022-01, whose financial support is gratefully acknowledged.


  1. 1.
    Ji W, Waas A (2010) Fragmentation of an axially impacted slender rod. Europhys Lett 89:46003CrossRefADSGoogle Scholar
  2. 2.
    Triantafyllidis N, Schnaidt WC (1993) Comparison of microscopic and macroscopic instabilities in a class of two-dimensional periodic composites. J Mech Phys Solids 41:1533–1565CrossRefMATHADSGoogle Scholar
  3. 3.
    Triantafyllidis N, Bardenhagen S (1996) The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models. J Mech Phys Solids 44:1891–1928MathSciNetCrossRefMATHADSGoogle Scholar
  4. 4.
    Nestorović MD, Triantafyllidis N (2004) Onset of failure in finitely strained layered composites subjected to combined normal and shear loading. J Mech Phys Solids 52:941–974CrossRefMATHADSGoogle Scholar
  5. 5.
    Rosen BW (1965) Mechanics of composite strengthening. Fiber composite materials: papers presented at a seminar of the American Society for Metals, October 17 and 18, 1964, pp 37–75Google Scholar
  6. 6.
    Schuerch HU (1966) Prediction of compression strength in uniaxial boron fiber-metal matrix composite materials. AIAA J Propuls Power 4:102–106CrossRefGoogle Scholar
  7. 7.
    Argon AS (1972) Fracture of composites. Treatise Mater Sci Technol 1:79–114CrossRefGoogle Scholar
  8. 8.
    Budiansky B (1983) Micromechanics. Comput Struct 16:3–12CrossRefMATHGoogle Scholar
  9. 9.
    Budiansky B, Fleck NA (1993) Compressive failure of fiber composites. J Mech Phys Solids 41:183–211CrossRefADSGoogle Scholar
  10. 10.
    Fleck NA, Deng L, Budiansky B (1995) Prediction of kink width in compressed fibre composites. J Appl Mech 62:329–337CrossRefMATHGoogle Scholar
  11. 11.
    Kyriakides S, Arseculeratne R, Perry EJ, Liechti KM (1995) On the compressive failure of fiber reinforced composites. Int J Solids Struct 32:689–738CrossRefMATHGoogle Scholar
  12. 12.
    Vogler TJ, Hsu S-Y, Kyriakides S (2000) Composite failure under combined compression and shear. Int J Solids Struct 37:1765–1791CrossRefMATHGoogle Scholar
  13. 13.
    Piggott MR (1995) The effect of fibre waviness on the mechanical properties of unidirectional fibre composites: a review. Compos Sci Technol 53:201–205CrossRefGoogle Scholar
  14. 14.
    Narayanan S, Schadler LS (1999) Mechanisms of kink-band formation in graphite/epoxy composites: a micromechanical study. Compos Sci Technol 59:2201–2213CrossRefGoogle Scholar
  15. 15.
    Drapier S, Grandidier J-C, Potier-Ferry M (2001) A structural approach of plastic microbuckling in long fibre composites: comparison with theoretical and experimental results. International J Solids Struct 38:3877–3904CrossRefMATHGoogle Scholar
  16. 16.
    Violette MG , Schapery RA (2002) Time-dependent compressive strength of unidirectional viscoelastic composite materials. Mech Time-Depend Mater 6:133–145CrossRefADSGoogle Scholar
  17. 17.
    Basu S, Waas AM, Ambur DR (2006) Compressive failure of fiber composites under multi-axial loading. J Mech Phys Solids 54:611–634CrossRefMATHADSGoogle Scholar
  18. 18.
    Prabhakar P, Waas AM (2013) Interaction between kinking and splitting in the compressive failure of unidirectional fiber reinforced laminated composites. Compos Struct 98:85–92CrossRefGoogle Scholar
  19. 19.
    Guimard J-M, Allix O, Pechnik N, Thévenet P (2009) Energetic analysis of fragmentation mechanisms and dynamic delamination modelling in CFRP composites. Comput Struct 87:1022–1032CrossRefGoogle Scholar
  20. 20.
    Feld N, Allix O, Baranger E, Guimard J-M (2011) Micro-mechanical prediction of UD laminates behaviour under combined compression up to failure: influence of matrix degradation. J Compos Mater 45:2317–2333CrossRefGoogle Scholar
  21. 21.
    Prabhakar P, Waas AM (2013) Micromechanical modeling to determine the compressive strength and failure mode interaction of multidirectional laminates. Composites A 50:11–21CrossRefGoogle Scholar
  22. 22.
    Vogler TJ, Kyriakides S (2001) On the initiation and growth of kink bands in fiber composites: Part I: experiments. Int J Solids Struct 38:2639–2682CrossRefMATHGoogle Scholar
  23. 23.
    Lapusta YN, Harich J, Wagner W (2008) Three-dimensional FE model for fiber interaction effects during microbuckling in composites with isotropic and anisotropic fibers. Commun Numer Methods Eng 24:2206–2215CrossRefMATHGoogle Scholar
  24. 24.
    Pimenta S, Gutkin R, Pinho ST, Robinson P (2009) A micromechanical model for kink-band formation: Part I—experimental study and numerical modelling. Compos Sci Technol 69:948–955CrossRefGoogle Scholar
  25. 25.
    Ladevèze P, Lubineau G, Violeau D (2006) A computational damage micromodel of laminated composites. Int J Fract 137:139–150CrossRefMATHGoogle Scholar
  26. 26.
    Laurin F, Carrère N, Maire J-F (2009) In: Olivier P, Lamon J (eds) Multiscale hybrid failure approach for strength analysis of composite structures subjected to complex 3D loadings. Comptes Rendus des JNC 16, ToulouseGoogle Scholar
  27. 27.
    Bouvet C, Castani B, Bizeul M, Barrau J-J (2009) Low velocity impact modelling in laminate composite panels with discrete interface elements. Int J Solids Struct 46:2809–2821CrossRefMATHGoogle Scholar
  28. 28.
    Wisnom MR (2010) Modelling discrete failures in composites with interface elements. Composites A 41:795–805CrossRefGoogle Scholar
  29. 29.
    van der Meer FP, Sluys LJ (2010) Mesh-independent modeling of both distributed and discrete matrix cracking in interaction with delamination in composites. Eng Fract Mech 77:719–735CrossRefGoogle Scholar
  30. 30.
    van der Meer FP, Oliver C, Sluys LJ (2010) Computational analysis of progressive failure in a notched laminate including shear nonlinearity and fiber failure. Compos Sci Technol 70:692–700CrossRefGoogle Scholar
  31. 31.
    van der Meer FP, Sluys LJ, Hallett SR, Wisnom MR (2012) Computational modeling of complex failure mechanisms in laminates. J Compos Mater 46:603–623CrossRefGoogle Scholar
  32. 32.
    Lee SH, Yerramalli CS, Waas AM (2000) Compressive splitting response of glass-fiber reinforced unidirectional composites. Compos Sci Technol 60:2957–2966CrossRefGoogle Scholar
  33. 33.
    Violeau D (2007) Une stratégie de calcul pour l’analyse à à l’ échelle “micro” des endommagements jusqu’ à à rupture des composites stratifiés. PhD Thesis, ENS CachanGoogle Scholar
  34. 34.
    Violeau D, Ladevèze P, Lubineau G (2009) Micromodel-based simulations for laminated composites. Compos Sci Technol 69:1364–1371CrossRefGoogle Scholar
  35. 35.
    Trovalet M (2010) Sur un modèle micro pour le calcul de structures en composites stratifiés. PhD Thesis, ENS Cachan, CachanGoogle Scholar
  36. 36.
    Hashin Z (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. J Mech Phys Solids 44:1129–1145CrossRefADSGoogle Scholar
  37. 37.
    Nairn JA, Hu S (1992) The initiation and growth of delaminations induced by matrix microcracks in laminated composites. Int J Fract 57:1–24CrossRefADSGoogle Scholar
  38. 38.
    Nairn JA (2000) Polymer matrix composites, vol 2 of comprehensive composite materials, chap 13: matrix microcracking in composites. Elsevier Science, AmsterdamGoogle Scholar
  39. 39.
    Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech 2:61–72CrossRefGoogle Scholar
  40. 40.
    Guimard J-M, Allix O, Pechnik N, Thévenet P (2007) Statistical energy and failure analysis of CFRP compression behavior using a uniaxial microbuckling model. J Compos Mater 41:2807–2828CrossRefGoogle Scholar
  41. 41.
    Sivashanker S, Fleck NA, Sutcliffe MPF (1996) Microbuckle propagation in a unidirectional carbon fibre-epoxy matrix composite. Acta Mater 44:2581–2590CrossRefGoogle Scholar
  42. 42.
    Schapery RA (1995) Prediction of compressive strength and kink bands in composites using a work potential. Int J Solids Struct 32:739–765Google Scholar
  43. 43.
    Feld N, Allix O, Baranger E, Guimard J-M (2012) A micromechanics-based mesomodel for unidirectional laminates in compression up to failure. J Compos Mater 46:2893–2909CrossRefGoogle Scholar
  44. 44.
    Pineda EJ, Waas AM (2013) Numerical implementation of a multiple-ISV thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates. Int J Fract 182:93–122CrossRefGoogle Scholar
  45. 45.
    Ladevèze P, Loiseau O, Dureisseix D (2001) A micro–macro and parallel computational strategy for highly heterogeneous structures. Int J Numer Methods Eng 52:121–138CrossRefGoogle Scholar
  46. 46.
    Kerfriden P, Allix O, Gosselet P (2009) A three-scale domain decomposition method for the 3D analysis of debonding in laminates. Comput Mech 44:343–362CrossRefMATHGoogle Scholar
  47. 47.
    Allix O, Kerfriden P, Gosselet P (2010) On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework. Int J Numer Methods Eng 83:1518–1540CrossRefMATHGoogle Scholar
  48. 48.
    Guidault P-A, Allix O, Champaney L, Navarro JP (2007) A two-scale approach with homogenization for the computation of cracked structures. Comput Struct 85:1360–1371MathSciNetCrossRefGoogle Scholar
  49. 49.
    Gendre L, Allix O, Comte F (2009) Non-intrusive and exact global/local techniques for structural problems with local plasticity. Comput Mech 44:233–245MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Gendre L, Allix O, Gosselet P (2011) A two-scale approximation of the schur complement and its use for non-intrusive coupling. Int J Numer Methods Eng 87:889–905MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Ladevèze P, Lubineau G (2003) On a damage mesomodel for laminates: micromechanics basis and improvement. Mech Mater 35:763–775CrossRefGoogle Scholar
  52. 52.
    Daghia F, Ladevèze P (2012) A micro-meso computational strategy for the prediction of the damage and failure of laminates. Compos Struct 94:3644–3653CrossRefGoogle Scholar
  53. 53.
    Hereil PL, Allix O, Gratton M (1997) Shock behaviour of 3D carbon–carbon composite. J Phys IV C3:529–534Google Scholar
  54. 54.
    Allix O, Dommanget M, Gratton M, Hreil PL (2001) A multi-scale approach for the response of a 3D carbon/carbon composite under shock loading. Compos Sci Technol 61:409–415CrossRefGoogle Scholar
  55. 55.
    Dvorak GJ, Laws N (1987) Analysis of progressive matrix cracking in composite laminates II. First ply failure. J Compos Mater 21:309–329CrossRefGoogle Scholar
  56. 56.
    Ladevèze P (1986) Sur la mécanique de l’endommagement des composites, vol 5. Comptes-rendus des Journées Nationales sur les Composites, Paris, pp 667–683Google Scholar
  57. 57.
    Schapery RA (1969) On the characterization of nonlinear viscoelastic media. Polym Eng Sci 9:295–310CrossRefGoogle Scholar
  58. 58.
    Lemaître J (1985) Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51:31–49CrossRefMATHADSGoogle Scholar
  59. 59.
    Ladevèze P (1989) On a damage mechanics approach. Mech Mech Damage Compos Multi-Mater 1:119–141Google Scholar
  60. 60.
    Paluch B (1994) Analysis of geometric imperfections in fibres for unidirectional fibre-reinforced composites. La Recherche Aéronautique 6:431–448Google Scholar
  61. 61.
    Yerramalli CS, Waas AM (2003) A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading. Int J Solids Struct 40:1139–1164CrossRefMATHGoogle Scholar
  62. 62.
    Gutkin R, Pinho ST, Robinson P, Curtis PT (2011) A finite fracture mechanics formulation to predict fibre kinking and splitting in CFRP under combined longitudinal compression and in-plane shear. Mech Mater 43:730–739CrossRefGoogle Scholar
  63. 63.
    Soutis C, Fleck NA (1990) Static compression failyre of carbon fibre T800/924C composite plate with a single hole. J Compos Mater 24:536–558CrossRefGoogle Scholar
  64. 64.
    Soutis C, Fleck NA, Smith PA (1991) Failure prediction technique for compression loaded carbon fibre-epoxy laminate with open holes. J Compos Mater 25:1476–1498Google Scholar
  65. 65.
    Soutis C, Curtis PT, Fleck NA (1993) Compressive failure of notched carbon fibre composites. Proc Math Phys Sci 440:241–256CrossRefGoogle Scholar
  66. 66.
    Soutis C, Curtis PT (2000) A method for predicting the fracture toughness of CFRP laminates failing by fibre microbuckling* 1. Composites A Appl Sci Manuf 31:733–740CrossRefGoogle Scholar
  67. 67.
    Lee J, Soutis C (2005) Thickness effect on the compressive strength of T800/924C carbon fibre-epoxy laminates. Composites A Appl Sci Manuf. 36:213–227CrossRefGoogle Scholar
  68. 68.
    Lee J, Soutis C (2008) Measuring the notched compressive strength of composite laminates: specimen size effects. Compos Sci Technol 68:2359–2366CrossRefGoogle Scholar
  69. 69.
    Jumahat A, Soutis C, Jones FR, Hodzic A (2010) Fracture mechanisms and failure analysis of carbon fibre/toughened epoxy composites subjected to compressive loading. Compos Struct 92:295–305CrossRefGoogle Scholar
  70. 70.
    Jumahat A, Soutis C, Hodzic A (2011) A graphical method predicting the compressive strength of toughened unidirectional composite laminates. Appl Compos Mater 18:65–83CrossRefADSGoogle Scholar
  71. 71.
    Ladevèze P, Lubineau G (2001) On a damage mesomodel for laminates micro–meso relationships, possibilities and limits. Compos Sci Technol 61:2149–2158CrossRefGoogle Scholar
  72. 72.
    Ladevèze P, Lubineau G, Marsal D (2006) Towards a bridge between the micro- and mesomechanics of delamination for laminated composites. Compos Sci Technol 66:698–712CrossRefGoogle Scholar
  73. 73.
    Lubineau G, Ladevèze P (2008) Construction of a micromechanics-based intralaminar mesomodel, and illustrations in abaqus/standard. Comput Mater Sci 43:137–145CrossRefGoogle Scholar
  74. 74.
    Allix O (2001) A composite damage meso-model for impact problems. Compos Sci Technol 61:2193–2205CrossRefGoogle Scholar
  75. 75.
    Allix O (2013) The bounded rate concept: a framework to deal with objective failure predictions in dynamic within a local constitutive model. Int J Damage Mech 22:808–828CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Olivier Allix
    • 1
  • Nicolas Feld
    • 2
  • Emmanuel Baranger
    • 1
  • Jean-Mathieu Guimard
    • 3
  • Cuong Ha-Minh
    • 1
  1. 1.LMT-Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud ParisCachanFrance
  2. 2.Peugeot-Citroën Automobiles, Direction ScientifiqueVelizy-VillacoublayFrance
  3. 3.EADS France, Innovation Works, Mechanical Modelling TeamSuresnesFrance

Personalised recommendations