Shear Bands in Isotropic Micropolar Elastic Materials

  • M. N. L. Narasimhan
  • M. Kumazawa
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 39)


This investigation concerns localized deformation fields occurring due to jumps of second-order gradients of displacement across a standing singular surface in a micropolar elastic material. Such a standing singular surface gives rise to a shear band. The condition for the existence of a shear band is obtained in terms of an appropriate acoustic tensor for the micropolar continuum. The behavior of the inclination angle of the shear band is examined under varied loading conditions. Numerical calculations are presented for a micropolar elastic solid in the two cases of uniaxial tension and of tension of a thin plate.


Shear Band Thin Plate Uniaxial Tension Couple Stress Singular Surface 
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.
    Hadamard, J. Lecons sur la Propagation des Ondes et les Equations de l’Hydrodynamique, Hermann, Paris (1903).MATHGoogle Scholar
  2. 2.
    Thomas, T. Y. Plastic Flow and Fracture in Solids, Academic Press, New York (1961).MATHGoogle Scholar
  3. 3.
    Hill, R. J. Mech. Phys. Solids 10, 1 (1962).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Hill, R. and Hutchinson, J. W. J. Mech. Phys. Solids 23, 239 (1975).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Tvergaard, V., Needleman, A.,and Lo, K. K. J. Mech. Phys. Solids 29, 115 (1981).CrossRefMATHGoogle Scholar
  6. 6.
    Biot, M. A. Mechanics of Incremental Deformations, John Wiley and Sons, New York (1965).Google Scholar
  7. 7.
    Tokuoka, T. Int. J. Engng. Sci. 24, No. 1, 41 (1986).CrossRefGoogle Scholar
  8. 8.
    Coleman, B. D. and Hodgdon, M. L. Arch. Ration. Mech. Anal. 90, 219 (1985).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Kafadar, C. B. and Eringen, A. C. Int. J. Engng. Sci. 9, 271 (1971).CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • M. N. L. Narasimhan
    • 1
  • M. Kumazawa
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA

Personalised recommendations