Analytical Evidence of Shear Band Bifurcations for Softening Materials

  • D. CaillerieEmail author
  • R. Chambon
  • Frédéric Collin
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG, volume 11)


Strain localization is a phenomenon occurring very often in anelastic media close to rupture and it is very important to take it into account in most of applications, particularly in geotechnics. Strain localization has been widely studied experimentally, see for instance Desrues (2004) or Desrues and Viggiani (2004). It has also been put in evidence in finite element simulations even if it presents mesh dependencies, see Chambon et al. (2001) for instance. From a theoretical point of view, the Rice condition (Rice 1976; Rudnicki and Rice 1975), with some assumptions, enables to determine the onset of strain localization but does not necessarily prove the existence of shear bands.


Shear band Analytical solution Bifurcation Softening Deformation theory of plasticity 


  1. B. Budiansky, A reassment of deformation theories of plasticity. J. Appl. Mech. 26, 259–264 (1959)MathSciNetGoogle Scholar
  2. R. Chambon, D. Caillerie, N. El Hassan, One dimensional localization studied with a second grade model. Eur. J. Mech. A/Solids 17(4), 637–656 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  3. R. Chambon, S. Crochepeyre, R. Charlier, An algorithm and a method to search bifurcation points in non-linear problems. Int. J. Numer. Methods Eng. 51, 315–332 (2001)zbMATHCrossRefGoogle Scholar
  4. J. Desrues, Tracking strain localization in geomaterials using computerized tomography. in Proceedings of the International Workshop on X-ray CT for Geomaterials Kumamoto, Japan, November 6–7 2003 (Balkema, Lisse, 2004), pp. 15–41Google Scholar
  5. J. Desrues, G. Viggiani, Strain localization in sand : an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2004)CrossRefGoogle Scholar
  6. J. Rice, The localization of plastic deformation, in International Congress of Theoretical and Applied Mechanics, ed. by W.D. Koiter (North Holland, Amsterdam, 1976)Google Scholar
  7. J.W. Rudnicki, J.R. Rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solids 23, 371–394 (1975)Google Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Laboratoire Sols Solides Structures – RisquesGrenoble Université & CNRSGrenoble CedexFrance
  2. 2.Université de Liège, ArGEnCo – Geo3LiègeBelgium

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