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Tytuł artykułu

The effect of surface elasticity on a Mode-III interface crack

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the contribution of surface elasticity to the anti-plane deformations of a linearly elastic bi-material with Mode-III interface crack. The surface elasticity is incorporated using a version of the continuum-based surface/interface model of Gurtin and Murdoch. We obtain a complete semi-analytic solution valid throughout the solid (including the crack tips) via a Cauchy singular, integro-differential equation of the first kind. Our solution demonstrates that the surface elasticity on the crack face leads to finite stresses at the crack tips and stress discontinuities across the material interface.
Rocznik
Strony
267--267
Opis fizyczny
–-286, Bibliogr. 13 poz.
Twórcy
autor
autor
autor
Bibliografia
  • 1. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Arch. Ration. Mech. Anal., 57, 4, 291–323, 1975.
  • 2. M.E. Gurtin, J. Weissmuller, F. Larche, A general theory of curved deformable interface in solids at equilibrium, Philos. Mag. A, 78, 5, 1093–1109, 1998.
  • 3. C.I. Kim, P. Schiavone, C.Q. Ru, The effects of surface elasticity on an elastic solid with mode-III crack: complete solution, ASME J. Appl. Mech., 77, 2, 021011 (1–7), 2009.
  • 4. C.I. Kim, P. Schiavone, C.Q. Ru, Analysis of plane-strain crack problems (mode-I and mode-II) in the presence of surface elasticity, J. Elasticity, doi: 10.1007/s10659-010-9287-0, 2010.
  • 5. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen, The Netherlands, 1953.
  • 6. A. Chakrabarti, Hamsapriye, Numerical solution of a singular integro-differential equation, ZAMM. Z. Agnew. Math. Mech., 79, 4, 233–241, 1999.
  • 7. A.H. England, Complex Variable Methods in Elasticity, John Wiley & Sons Ltd., London 1971.
  • 8. F.D. Gakhov, Boundary value problems, Pergamon Press, Oxford 1963.
  • 9. C-Q. Ru, Simple geometrical explanation of Gurtin–Murdoch model of surface elasticity with clarification of its related versions, Science China, 53, 3, 536–544, 2010.
  • 10. A. Chakrabarti, A.J. George, Solution of a singular integral equation involving two intervals arising in the theory of water waves, Appl. Math. Lett., 7, 5, 43–47, 1994.
  • 11. A.C. Kaya, F. Erdogan, On the solution of integral equations with a generalized Cauchy kernel, Quart. Appl. Math., XLV, 3, 455–469, 1987.
  • 12. P. Sharma, S. Ganti, Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface engergies, JASME J. Appl. Mech., 71, 5, 663–671, 2004.
  • 13. L. Tian, R.K.N.D. Rajapakse, Analytical solution of size-dependent elastic field of a nano-scale circular inhomogeneity, JASME J. Appl. Mech., 74, 3, 568–574, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0010-0021
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