Skip to main content

Non-local Damage-Enhanced MFH for Multiscale Simulations of Composites

  • Conference paper
  • First Online:
Composite Materials and Joining Technologies for Composites, Volume 7

Abstract

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient computational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fibers directions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kanouté P, Boso D, Chaboche J, Schrefler B (2009) Multiscale methods for composites: a review. Arch Comput Method Eng 16:31–75

    Article  MATH  Google Scholar 

  2. Geers M, Kouznetsova V, Brekelmans WAM (2010) Multi-scale computational homogenization: trends and challenges. J Comput Appl Math 234:2175–2182

    Article  MATH  Google Scholar 

  3. Doghri I, Brassart L, Adam L, Gérard JS (2011) A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites. Int J Plast 27(3):352–371

    Article  MATH  Google Scholar 

  4. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond Ser A Math Phys Sci 241(1226):376–396

    Article  MathSciNet  MATH  Google Scholar 

  5. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574

    Article  Google Scholar 

  6. Benveniste Y (1987) A new approach to the application of Mori-Tanaka’s theory in composite materials. Mech Mater 6(2):147–157

    Article  MathSciNet  Google Scholar 

  7. Kröner E (1958) Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Zeitschrift f¨ur Phys A Hadrons Nucl 151:504–518

    Article  Google Scholar 

  8. Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222

    Article  Google Scholar 

  9. Hill R (1965) Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids 13(2):89–101

    Article  MATH  Google Scholar 

  10. Pettermann HE, Plankensteiner AF, Böhm HJ, Rammerstorfer FG (1999) A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori-Tanaka approach. Comput Struct 71(2):197–214

    Article  Google Scholar 

  11. Doghri I, Ouaar A (2003) Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms. Int J Solids Struct 40(7):1681–1712

    Article  MATH  Google Scholar 

  12. Chaboche J, Kanouté P, Roos A (2005) On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites. Int J Plast 21(7):1409–1434

    Article  MATH  Google Scholar 

  13. Wu L, Noels L, Adam L, Doghri I (Submitted) Multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage model. Comput Method Appl Mech Eng

    Google Scholar 

  14. Peerlings R, Geers M, de Borst R, Brekelmans W (2001) A critical comparison of nonlocal and gradient-enhanced softening continua. Int J Solids Struct 38:7723–7746

    Article  MATH  Google Scholar 

  15. Geers M (1997) Experimental analysis and computational modelling of damage and fracture, Ph.D. thesis. University of Technology, Eindhoven (Netherlands)

    Google Scholar 

  16. Wu L, Noels L, Adam L, Doghri I (in preparation)Anisotropic gradient-enhanced damage mean-field homogenization for multiscale analysis of composite laminates

    Google Scholar 

  17. Lemaitre J, Desmorat R (2005) Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer, Berlin. ISBN 3540215034

    Google Scholar 

Download references

Acknowledgement

The research has been funded by the Walloon Region under the agreement SIMUCOMP n° 1017232 (CT-EUC 2010-10-12) in the context of the ERA-NET +, Matera + framework.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ling Wu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Wu, L., Noels, L., Adam, L., Doghri, I. (2013). Non-local Damage-Enhanced MFH for Multiscale Simulations of Composites. In: Patterson, E., Backman, D., Cloud, G. (eds) Composite Materials and Joining Technologies for Composites, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4553-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-4553-1_13

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4552-4

  • Online ISBN: 978-1-4614-4553-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics