Recent Extensions of Gurson’s Model for Porous Ductile Metals

  • M. Gologanu
  • J.-B. Leblond
  • G. Perrin
  • J. Devaux
Part of the International Centre for Mechanical Sciences book series (CISM, volume 377)


This paper is devoted to two distinct extensions of Gurson’s (1977) famous model for plastic voided metals. Gurson’s work was based on an approximate limit-analysis of a typical elementary volume in a porous material, namely a hollow sphere subjected to conditions of arbitrary homogeneous boundary strain rate. The first extension envisaged consists in considering a more general geometry, namely a spheroidal volume containing some spheroidal confocal cavity. The aim here is to incorporate void shape effects into Gurson’s model. The second extension again considers a hollow sphere, but now subjected to conditions of inhomogeneous boundary strain rate. The goal is to account for possible strong variations of the macroscopic mechanical fields at the scale of the representative cell (i.e. of the void spacing), as encountered near crack tips.


Hollow Sphere Yield Locus Spherical Void Recent Extension Axisymmetric Loading 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Budiansky, B., Hutchinson, J.W., and Slutsky, S., 1982, Void growth and collapse in viscous solids, in Mechanics of Solids, Hopkins and Sewell, eds., Pergamon Press, Oxford, pp. 13–45.Google Scholar
  2. Drugan, W.J., and Willis, J.R., 1996, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, J. Mech. Phys. Solids, 44, 497–524.CrossRefGoogle Scholar
  3. Garajeu, M., 1995, Contribution à l’étude du comportement non linéaire de milieux poreux avec ou sans renfort, Thèse de Doctorat, Université de la Méditerranée, Marseille.Google Scholar
  4. Germain, P., 1973a, La méthode des puissances virtuelles en mécanique des milieux continus. Première partie: Théorie du second gradient, J. Mécanique, 12, 235–274.Google Scholar
  5. Germain, P., 1973b, The method of virtual power in continuum mechanics. Part 2: Microstructure, SIAM J. Appl. Math., 25, 556–575.CrossRefGoogle Scholar
  6. Gologanu, M., 1996, Thèse de Doctorat, in preparation, Université Pierre et Marie Curie, Paris.Google Scholar
  7. Gologanu, M., Leblond, J.B., and Devaux, J., 1993, Approximate models for ductile metals containing non-spherical voids–Case of axisymmetric prolate ellipsoidal cavities, J. Mech. Phys. Solids, 41, 1723–1754.CrossRefGoogle Scholar
  8. Gologanu, M., Leblond, J.B., and Devaux, J., 1994, Approximate models for ductile metals containing non-spherical voids–Case of axisymmetric oblate ellipsoidal cavities, ASME J. Eng. Mat. Tech., 116, 290–297.CrossRefGoogle Scholar
  9. Gradshteyn, I.S., and Ryzhik, I.M., 1980, Table of Integrals, Series, and Products, Academic Press, New-York.Google Scholar
  10. Gurson, A.L., 1977, Continuum theory of ductile rupture by void nucleation and growth: Part I–Yield criteria and flow rules for porous ductile media, ASME J. Eng. Mat. Tech., 99, 2–15.CrossRefGoogle Scholar
  11. Hill, R., 1967, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, 15, 79–95.CrossRefGoogle Scholar
  12. Koplik, J., and Needleman, A., 1988, Void growth and coalescence in porous plastic solids, Int. J. Solids Structures, 24, 835–853.CrossRefGoogle Scholar
  13. Leblond, J.B., and Perrin, G., 1995, Introduction à la mécanique de la rupture ductile des métaux, Cours de l’Ecole Polytechnique, Paris.Google Scholar
  14. Leblond, J.B., Perrin, G., and Devaux, J., 1994, Bifurcation effects in ductile metals with nonlocal damage, ASME J. Appl. Mech., 61, 236–242.CrossRefGoogle Scholar
  15. Lee, B.J., and Mear, M.E., 1992, Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids, J. Mech. Phys. Solids, 40, 1805–1836.CrossRefGoogle Scholar
  16. Mandel, J., 1964, Contribution théorique à l’étude de l’écrouissage et des lois d’écoulement plastique, in Proceedings of the 11th International Congress on Applied Mechanics, Springer, Berlin, pp. 502–509.Google Scholar
  17. Mazataud, P., 1995, private communication.Google Scholar
  18. Mindlin, R.D., 1964, Microstructure in linear elasticity, Archives Rat. Mech. Anal., 16, 51–78.Google Scholar
  19. Mindlin, R.D., and Eshel, N.N., 1968, On first strain-gradient theories in linear elasticity, Int. J. Solids Structures, 4, 109–124.CrossRefGoogle Scholar
  20. Mura, T., 1982, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague.CrossRefGoogle Scholar
  21. Pijaudier-Cabot, G., and Bazant, Z.P., 1987, Nonlocal damage theory, ASCE J. Eng. Mech., 113, 1512–1533.CrossRefGoogle Scholar
  22. Pineau, A., and Joly, P., 1991, Local versus global approaches of elastic-plastic fracture mechanics. Application to ferritic steels and a cast duplex stainless steel, in Defects Assessment in Components - Fundamentals and Applications, Blauel and Schwalbe, eds., ESIS, EGF publication 9.Google Scholar
  23. Ponte-Castaneda, P., and Zaidman, M., 1994, Constitutive models for porous materials with evolving microstructure, J. Mech. Phys. Solids, 42, 1459–1495.CrossRefGoogle Scholar
  24. Sovik, O.P., 1995, private communication.Google Scholar
  25. Suquet, P., 1982, Plasticité et homogénéisation, Thèse de Doctorat d’Etat, Université Pierre et Marie Curie, Paris.Google Scholar
  26. Suquet, P., and Ponte-Castaneda, P., 1993, Small-contrast perturbation expansions for the effective properties on nonlinear composites, C. R. Acad. Sci. Paris, Série II, 317, 1515–1522.Google Scholar
  27. Tvergaard, V., and Needleman, A., 1995, Effects of nonlocal damage in porous plastic solids, Int. J. Solids Structures, 32, 1063–1077.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • M. Gologanu
    • 1
  • J.-B. Leblond
    • 1
  • G. Perrin
    • 2
  • J. Devaux
    • 3
  1. 1.University of Paris VIParisFrance
  2. 2.Bureau de Contrôle des Chaudières NucléairesDijonFrance
  3. 3.FRAMASOFT+CSILyonFrance

Personalised recommendations