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Effects of boundary reinforcement on local singular fields in linearly elastic materials

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the local deformation near a point at the interface between free and fixed boundary segments in an elastic half-plane undergoing plane strain deformations. Using asymptotic analysis, we show that the addition of a reinforcement along the free boundary effectively eliminates the well-known oscillatory behavior of the displacement and stress fields in the vicinity of the point leading to a strong square-root stress singularity. In addition, we demonstrate that the reinforcement induces a deformation field which is smooth locally and bounded at the point of interest.
Rocznik
Strony
289--–300
Opis fizyczny
Bibliogr. 24 poz., wykr.
Twórcy
autor
  • Department of Mechanical Engineering University o f Alberta, Edmonton Alberta T6G 2G8, Canada
autor
  • Department of Mechanical Engineering University o f Alberta, Edmonton Alberta T6G 2G8, Canada
autor
  • Department of Mechanical Engineering University o f Alberta, Edmonton Alberta T6G 2G8, Canada
Bibliografia
  • 1. D. J. Steigmann, R.W. Ogden, Piane deformations of elastic solids with intrinsic boundary elasticity, Proc. R. Soc. Lond. A, 453, 853-877, 1997.
  • 2. D. J.Steigmann, R.W. Ogden, A necessary condition for energy-minimizing plane deformations of elastic solids with intrinsic boundary elasticity, Math. Mech. Solids, 2, 3-16, 1997.
  • 3. D. J. Steigmann, R. W. Ogden, Elastic surface-substrate interactions, Proc. R. Soc. Lond. A, 455, 437-474, 1999.
  • 4. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Arch. Kation. Mech. Anal., 57, 4, 291-323, 1975.
  • 5. P. Chhapadia, P. Mohammadi, P. Sharma, Curvature- dependent surface energy and implications for nanostructures, J. Mech. Phys. Solids, 59, 2103-2115, 2011.
  • 6. P. Schiavone, C. Q. Ru, Integral equation methods in plane-strain elasticity with boundary reinforcement, Proc. R. Soc. Lond. A, 454, 2223-2242, 1998.
  • 7. E. Orowan, Surface energy and surface tension in solids and fluids, Proc. R. Soc. Lond. A, 316, 473-491, 1970.
  • 8. M.E. Gurtin, A.I. Murdoch, Surface stress in solids, Int. J. Solids Struct., 14, 431-440, 1978.
  • 9. J.W. Chan, F. Larche, Surface stress and chemical equilibrium of smali crystals - II. Solid particles embedded in a solid matrix, Acta Metali., 30, 51-56, 1982.
  • 10. Y. Benveniste, J. Aboudi, Continuum model for fiber reinforced materials with debonding, Int. J. Solids Struct., 20, 11-12, 935-951, 1984.
  • 11. R. Thomson, T. J. Chuang, The role of surface stress in fracture, Acta Metali., 34, 6, 1133-1143, 1986.
  • 12. R. C. Cammarata, Surface and interface stress effects in thin films, Progress. Surf. Science, 46, 1-38, 1994.
  • 13. H. Altenbach, V.A. Eremeyev, L.P. Lebedev, On the existence of solution in linear elasticity with surface stresses, Z. Angew. Math. Mech., 90, 7, 535-536, 2010.
  • 14. H. Altenbach, V.A. Eremeyev, L.P. Lebedev, On the spectrum and stiffness of an elastic body with surface stresses, Z. Angew. Math. Mech., 91, 9, 699-710, 2010.
  • 15. H.X. zhu, The effects of surface and initial stresses on the bending stiffness of nanowires, Nanotechnology, 19, Art. 405703, 2008.
  • 16. G.F.Wang, X.Q. Feng, S.W. Yu, Surface buckling of a bending microbeam due to surface elasticity, Europhysics Letters, 77, Art. 44002, 2007.
  • 17. Z.Q. Wang, Y.P Zhao, Z.P. Huang, The effects of surface tension on the elastic properties of nanostructures, Int. J. Eng. ScL, 48, 140—150, 2010.
  • 18. J.S. Wang, Y.H. Cui, X.Q. Feng, G.F. Wang, Q.H. Qin, Surface Effects on the Elasticity of Nanosprings, Europhysics Letters, 92, 16002-1-6, 2010.
  • 19. H. Altenbach, V. A. Eremeyev, N. F. Morozov, Linear theory o f shells taking into account surface stresses, Doklady Physics, 54, 531-535, 2009.
  • 20. H. Altenbach, V.A. Eremeyev, N.F. Morozov, On equations of the linear theory of shells with surface stresses taken into account, Mechanics of Solids, 45, 331-342, 2010.
  • 21. X. Wang, P. Schiavone, Firnie matrix crack penetrating a partially debonded circular inhomogeneity, Arch. Mech., 64, 3, 319-342, 2012.
  • 22. J. K. Knowles, E. Sternberg, On the singularity induced by certain mixed Bondary conditions in linearized and noniinear elastostatics, Int. J. Solids Structures, 11, 1173-1201, 1975.
  • 23. N.I. Muskhelishvili, Some basic problems o f the mathematical theory of elasticity, Noordhoff, Groningen, Netherlands, 1963.
  • 24. M. L. Williams, Stress singularities resulting from yarious boundary conditions in angular comers of plates in extension, J. Appl. Mech., 66, 556-560, 1952.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-307321f1-1f65-4ae3-96e4-e728252659e0
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