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International Journal of Fracture

, Volume 79, Issue 2, pp 107–119 | Cite as

Cracks in gradient elastic bodies with surface energy

  • G. Exadaktylos
  • I. Vardoulakis
  • E. Aifantis
Article

Abstract

In the present paper the effect of higher order gradients on the structure of line-crack tips is determined. In particular we introduce in the constitutive equations of the linear deformation of an elastic solid a volumetric energy term, which includes the contribution of the strain gradient, and a surface energy gradient dependent term and then determine the effect of these terms on the structure of the mode-III crack tip and the associated stress and strain fields. By making use of the solution in terms of Fourier transform of the equation of elastic equilibrium we solve the half-plane boundary value problems of: (a) specified tractions, and (b) prescribed displacements, along the crack surface, respectively.

Keywords

Fourier Transform Surface Energy Civil Engineer Constitutive Equation Crack 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.

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References

  1. 1.
    E.C.Aifantis, On the role of gradients in the localization of deformation and fracture, International Journal of Engineering Science 30(10) (1992) 1279–1299.Google Scholar
  2. 2.
    E.C.Aifantis, Gradient effects at macro, micro, and nano scales, Journal of Mechanical Behavior of Materials 5 (1994) 355–375.Google Scholar
  3. 3.
    B.S.Altan and E.C.Aifantis, On the structure of the mode-III crack-tip in gradient elasticity, Scripta Metallurgica et Materialia 1 (1992) 319–324.Google Scholar
  4. 4.
    G.I.Barenblatt, Mathematical theory of equilibrium cracks in brittle fracture, Advances in Applied Mechanics 7 (1962) 55.Google Scholar
  5. 5.
    P.Casal, La capilarite interne, Cahier du Groupe Francais d'Etudes de Rheologie C.N.R.S. VI (3), (1961) 31–37.Google Scholar
  6. 6.
    I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series, and Products, Corrected and Enlarged Edition, Alan Jeffrey (ed.) Academic Press (1980).Google Scholar
  7. 7.
    R.D.Mindlin, Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures 1 (1965) 417–438.Google Scholar
  8. 8.
    C.Q.Ru and E.C.Aifantis, A simple approach to solve boundary-value problems in gradient elasticity, Acta Mechanica 101 (1993) 59–68.Google Scholar
  9. 9.
    I.N.Sneddon, The distribution of surface stress necessary to produce a Griffith crack of prescribed shape, International Journal of Engineering Science 7 (1969) 875–882.Google Scholar
  10. 10.
    I. Vardoulakis, G. Exadaktylos, and E. Aifantis, Gradient elasticity with surface energy: Mode-III crack problem, International Journal of Solids and Structures, in press (1996).Google Scholar
  11. 11.
    I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics, Blackie Academic and Professional (1995).Google Scholar
  12. 12.
    C.H.Wu, Cohesive elasticity and surface phenomena, Quarterly of Applied Mathematics L(1), (1992) 73–103.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • G. Exadaktylos
    • 1
  • I. Vardoulakis
    • 2
  • E. Aifantis
    • 3
    • 4
  1. 1.Department of Mineral Resources EngineeringTechnical University of CreteHaniaGreece
  2. 2.Department of Engineering ScienceNational Technical University of AthensAthensGreece
  3. 3.Center for Mechanics of Materials and InstabilitiesMichigan Technological UniversityHoughtonUSA
  4. 4.Laboratory of Mechanics and MaterialsAristotle University of ThessalonikiThessalonikiGreece

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