Skip to main content
Log in

A three-scale domain decomposition method for the 3D analysis of debonding in laminates

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures results in very large numerical problems. In this paper, the exact mesoscale solution is sought using parallel iterative solvers. The LaTIn-based mixed domain decomposition method makes it very easy to handle the complex description of the structure; moreover the provided multiscale features enable us to deal with numerical difficulties at their natural scale; we present the various enhancements we developed to ensure the scalability of the method. An extension of the method designed to handle instabilities is also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Allix O, Corigliano A (1996) Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens. Int J Fract 77: 11–140

    Article  Google Scholar 

  2. Allix O, Ladevèze P (1992) Interlaminar interface modelling for the prediction of delamination. Comput Struct 22: 235–242

    Article  Google Scholar 

  3. Allix O, Lévêque D, Perret L (1998) Identification and forecast of delamination in composite laminates by an interlaminar interface model. Compos Sci Technol 58: 671–678

    Article  Google Scholar 

  4. Ben Dhia H, Rateau G (2005) The arlequin method as a flexible engineering design tool. Int J Numer Methods Eng 62(11): 1442–1462

    Article  MATH  Google Scholar 

  5. Cresta P, Allix O, Rey C, Guinard S (2007) Nonlinear localization strategies for domain decomposition methods in structural mechanics. Comput Methods Appl Mech Eng 196: 1436–1446

    Article  MathSciNet  Google Scholar 

  6. Crisfield MA (1981) A fast incremental iterative solution procedure that handles ’snap-through’. Comput Struct 13: 55–62

    Article  MATH  Google Scholar 

  7. De Borst R, Remmers JC (2006) Computational modelling of delamination. Compos Sci Technol 66: 713–722

    Article  Google Scholar 

  8. Dostál Z, Horák D, Vlach O (2007) Feti-based algorithms for modelling of fibrous composite materials with debonding. Math Comput Simul 76: 57–64

    Article  MATH  Google Scholar 

  9. Farhat C, Roux FX (1991) A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32: 1205–1227

    Article  MATH  Google Scholar 

  10. Feyel F, Chaboche J-L (2000) Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials. Comput Methods Appl Mech Eng 183: 309–330

    Article  MATH  Google Scholar 

  11. Fish J, Shek K, Pandheeradi M, Shephard MS (1997) Computational plasticity for composite structures based on mathematical homogenization: Theory and practice. Comput Methods Appl Mech Eng 148: 53–73

    Article  MATH  MathSciNet  Google Scholar 

  12. Germain N, Besson J, Feyel F, Gosselet P (2007) High-performance parallel simulation of structure degradation using non-local damage models. Int J Numer Methods Eng 71: 253–276

    Article  MathSciNet  Google Scholar 

  13. Ghosh S, Lee K, Raghavan P (2001) A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int J Solids Struct 38: 2335–2385

    Article  MATH  Google Scholar 

  14. Gosselet P, Rey C (2006) Non-overlapping domain decomposition methods in structural mechanics. Arch Comput Methods Eng 13: 515–572

    Article  MathSciNet  Google Scholar 

  15. Guidault P-A, Allix O, Champaney L, Cornuault S (2008) A multiscale extended finite element method for crack propagation. Comput Methods Appl Mech Eng 197(5): 381–399

    Article  Google Scholar 

  16. Hughes TJR, Feijoo GR, Mazzei L, Quincy J-B (1998) The variarional multiscale—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166: 3–24

    Article  MATH  MathSciNet  Google Scholar 

  17. Ladevèze P, Dureisseix D (2000) A micro/macro approch for parallel computing of heterogeneous structures. Int J Comput Civil Struct Eng 1: 18–28

    Google Scholar 

  18. Ladevèze P, Lubineau G (2002) An enhanced mesomodel for laminates based on micromechanics. Compos Sci Technol 62(4): 533–541

    Article  Google Scholar 

  19. Ladevèze P, Lubineau G, Violeau D (2006) A computational damage micromodel of laminated composites. Int J Fract 137: 139–150

    Article  Google Scholar 

  20. Ladevèze P, Néron D, Passieux J-C (2008) On multiscale computational mechanics with time-space homogenization. In: Fish J (ed) Bridging the scales in science and engineering. Oxford University Press, London (in press)

  21. Ladevèze P, Nouy A (2003) On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput Methods Appl Mech Eng 192: 3061–3087

    Article  MATH  Google Scholar 

  22. Mandel J (1993) Balancing domain decomposition. Commun Numer Methods Eng 9: 233–241

    Article  MATH  MathSciNet  Google Scholar 

  23. Melenk J, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 39: 289–314

    Article  Google Scholar 

  24. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Eng Sci 46: 131–150

    MATH  Google Scholar 

  25. Oden JT, Vemaganti K, Moës N (1999) Hierarchical modeling of heterogeneous solids. Comput Methods Appl Mech Eng 172: 3–25

    Article  MATH  Google Scholar 

  26. Oliver J, Huespe AE (2004) Continuum approach to material failure in strong discontinuity settings. Comput Methods Appl Mech Eng 193: 3195–3220

    Article  MATH  MathSciNet  Google Scholar 

  27. Pebrel J, Rey C, Gosselet P (2008) A nonlinear dual domain decomposition method: application to structural problems with damage. Int J Multiscale Comput Eng 6(3): 251–262

    Article  Google Scholar 

  28. Riks E (1972) The application of newton’s methods to the problem of the application of newton’s methods to the problem of elastic stability. Journal of Applied Mechanics 39: 1060–1065

    MATH  Google Scholar 

  29. Sanchez-Palencia E (1980) Non homogeneous media and vibration theory. Lecture notes in physics, vol 127. Springer, Berlin

  30. Schellenkens JCJ, De Borst R (1993) On the numerical integration of interface elements. Int J Numer Methods Eng 36(1): 43–66

    Article  Google Scholar 

  31. Stein E, Ohnimus S (1997) Coupled model- and solution-adaptivity in the finite-element method. Comput Methods Appl Mech Eng 150: 327–350

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Kerfriden.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kerfriden, P., Allix, O. & Gosselet, P. A three-scale domain decomposition method for the 3D analysis of debonding in laminates. Comput Mech 44, 343–362 (2009). https://doi.org/10.1007/s00466-009-0378-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-009-0378-3

Keywords

Navigation