Acta Mechanica

, Volume 101, Issue 1–4, pp 59–68 | Cite as

A simple approach to solve boundary-value problems in gradient elasticity

  • C. Q. Ru
  • E. C. Aifantis
Contributed Papers


We outline a procedure for obtaining solutions of certain boundary value problems of a recently proposed theory of gradient elasticity in terms of solutions of classical elasticity. The method is applied to illustrate, among other things, how the gradient theory can remove the strain singularity from some typical examples of the classical theory.


Dynamical System Fluid Dynamics Classical Theory Transport Phenomenon Simple Approach 
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]
    Aifantis, E. C.: On the microstructural origin of certain inelastic models. Trans. ASME. J. Mat. Eng. Tech.106, 326–330 (1984).Google Scholar
  2. [2]
    Aifantis, E. C.: The physics of plastic deformation. Int. J. Plasticity3, 211–247 (1987).Google Scholar
  3. [3]
    Triantafyllidis, N., Aifantis, E. C.: A gradient approach to localization of deformation-I. Hyperelastic materials. J. Elasticity16, 225–238 (1986).Google Scholar
  4. [4]
    Zbib, H., Aifantis, E. C.: On the localization and post-localization of plastic deformation. Part I. On the initiation of shear-bands; Part II. On the evolution and thickness of shear bands; Part III. On the structure and velocity of Portevin-Le Chatelier bands. Res Mechanica23 (Special Issue on Material Instabilities, Aifantis, E. C. et al., eds.), 261–277, 279–292, 293–305, (1988).Google Scholar
  5. [5]
    Altan, S. B., Aifantis, E. C.: On the structure of the mode-III crack-tip in gradient elasticity. Scripta Met.26, 319–324 (1992).Google Scholar
  6. [6]
    Love, A. E. H.: A treatise on mathematical theory of elasticity. New York: Dover 1944.Google Scholar
  7. [7]
    Sneddon, I. N.: Application of integral transforms in the theory of elasticity. CISM, No. 220, 1975.Google Scholar
  8. [8]
    Ru, C. Q., Aifantis, E. C.: In preparation.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • C. Q. Ru
    • 1
  • E. C. Aifantis
    • 1
  1. 1.Department of Mechanical Engineering and Engineering MechanicsMichigan Technological UniversityHoughtonUSA

Personalised recommendations