Multiscale Modelling of Non-Linear Behaviour of Heterogeneous Materials: Comparison of Recent Homogeneisation Methods

  • Pascale Kanouté
  • Jean-Louis Chaboche
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 114)


This paper aims at evaluating recent homogenisation methods for scale changes in the micro-to-macro elastoplastic analysis of composites as well as polycrystalline aggregate. The corresponding localisation rules are recalled including, the T.F.A scheme, the incremental tangent approach of Hill, and the more recent affine method. These different schemes are finally applied to predict the overall behaviour of metal-matrix composites. With the help of simulations performed by the Finite Element method, we will discuss the limitations and the advantages of these procedures.

Key words

Multiscale analysis Inhomogeneous material Non-Linear behaviour Homogenisation 


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  1. [1]
    G.I. Taylor, Plastic strains in metals, J. Inst. Metals, 62 307–324, 1938.Google Scholar
  2. [2]
    E. Kröner, Zur plastichen Verformung des Vielkristalls, Acta Metallo. 9, 155–161.Google Scholar
  3. [3]
    R. Hill, Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids., 13, 89–101.Google Scholar
  4. [4]
    M. Berveiller and A. Zaoui, An extension of the self-consistent scheme to plastically-flowing polycrystals, J. Mech. Phys. Solids., 26, 325–344, 1979.CrossRefGoogle Scholar
  5. [5]
    A. Molinari, G.R. Canova, and S. Ahzi, A self-consistent approach for the large deformation polycrystal viscoplasticity, Acta Metall, 35:2983–2994, 1987.CrossRefGoogle Scholar
  6. [6]
    G. Dvorak, Transformation fields analysis of inelastic composite materials, Proceedings of the Royal Society of London, A.437, 311–327, 1992.CrossRefGoogle Scholar
  7. [7]
    G. Dvorak, Y. Bahei-El-Din, A. Wafa, Implementation of the transformation field analysis for inelastic composite materials, Comput. Mech., 14, 201–228, 1994.CrossRefGoogle Scholar
  8. [8]
    R. Masson and A. Zaoui, Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials, J. Mech. Phys. Solids, 47, 1543–1568, 1999.CrossRefGoogle Scholar
  9. [9]
    R. Masson, M. Bornert, P. Suquet and A. Zaoui, An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals, J. Mech. Phys. Solids, 48:1203–1227, 2000.CrossRefGoogle Scholar
  10. [10]
    J. L. Chaboche, S. Kruch, J. F. Maire, T. Portier, Towards a micromechanics based inelastic and damage modeling of composites, International Journal of Plasticity, 17, 411–439, 2001.CrossRefGoogle Scholar
  11. [11]
    T. Pottier, Modélisation multiéchelle du comportement et Pendornrnagement de composites à matrice métallique. Doctorat d’Üniversite, Ecole nationale des Ponts et Chaussées, 1998.Google Scholar
  12. [12]
    P. Suquet, Effective properties of nonlinear composites, Continuum Micromechanics, P. Suquet Ed., Cism Lectures No. 377, Springer-Verlag, 197–264, 1997.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Pascale Kanouté
    • 1
  • Jean-Louis Chaboche
    • 1
  1. 1.ONERAChatillon CedexFrance

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