Material Instabilities in Elastic and Plastic Solids: The Perturbative Approach


The perturbative approach to material instabilities introduced by Bigoni and Capuani [2],[3] (in which a perturbing agent is superimposed to a uniformly stressed and strained infinite medium) is reviewed and applied to show how randomly-distributed dislocation-like defects can induce strain patterns in ductile metallic materials, prestressed near the border of ellipticity loss. These patterns result to be strongly focussed and organized into shear bands, evidencing a well-defined texture in the material.


Shear Band Concentrate Force Incremental Displacement Perturbative Approach Force Dipole 
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. 1.
    Bertoldi, K., Brun, M., Bigoni, D.: Int. J. Numer. Meth. Eng. 64, 877–906 (2005)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bigoni, D., Capuani, D.: J. Mech. Phys. Solids 50, 471–500 (2002)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Bigoni, D., Capuani, D.: J. Mech. Phys. Solids 53, 1163–1187 (2005)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Bigoni, D., Dal Corso, F.: Proc. R Soc. Lond. A 464, 2365–2390 (2008)MATHCrossRefGoogle Scholar
  5. 5.
    Bigoni, D., Dal Corso, F., Gei, M.: J. Mech. Phys. Solids 56, 839–857 (2008)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dal Corso, F., Bigoni, D.: Proc. R Soc. Lond. A (2008) (in press)Google Scholar
  7. 7.
    Dal Corso, F., Bigoni, D., Gei, M.: J. Mech. Phys. Solids 56, 815–838 (2008)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gajo, A., Bigoni, D., Muir Wood, D.: J. Mech. Phys. Solids 52, 2683–2724 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Hirth, J.P., Lothe, J.: Theory of dislocations. J. Wiley & Sons, New York (1968)Google Scholar
  10. 10.
    Hutchinson, J.W., Neale, K.W.: Finite strain J2-deformation theory. In: Carlson, D.E., Shield, R.T. (eds.) Proc. IUTAM Symp. on Finite Elasticity, Martinus Nijhoff, The Hague (1979)Google Scholar
  11. 11.
    Piccolroaz, A., Bigoni, D., Willis, J.R.: J. Mech. Phys. Solids 54, 2391–2417 (2006)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Poirier, C., Ammi, M., Bideau, D., Troadec, J.P.: Phys. Rev. Lett. 68, 216–219 (1992)CrossRefGoogle Scholar
  13. 13.
    Rice, J.R.: The localization of plastic deformation. In: Koiter, W.T. (ed.) Theoretical and Applied Mechanics, North-Holland, Amsterdam (1977)Google Scholar
  14. 14.
    Ryzhak, E.I.: J. Mech. Phys. Solids 41, 1345–1356 (1993)MATHCrossRefGoogle Scholar
  15. 15.
    Willis, J.R.: Inclusions and cracks in constrained anisotropic media. In: Wu, J.J., Ting, T.C.T., Barnett, D.M. (eds.) Modern Theory of Anisotropic Elasticity and Applications. SIAM, Philadelphia (1991)Google Scholar

Copyright information

© © Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical and Structural EngineeringUniversity of TrentoTrentoItaly

Personalised recommendations