Interaction and multiscale mechanics

  • 제4권2호
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  • Pages.85-105
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  • 2011
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Surface elasticity and residual stress effect on the elastic field of a nanoscale elastic layer

  • Intarit, P. (Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University) ;
  • Senjuntichai, T. (Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University) ;
  • Rungamornrat, J. (Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University) ;
  • Rajapakse, R.K.N.D. (Faculty of Applied Sciences, Simon Fraser University)
  • 투고 : 2010.11.19
  • 심사 : 2011.02.26
  • 발행 : 2011.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

The influence of surface elasticity and surface residual stress on the elastic field of an isotropic nanoscale elastic layer of finite thickness bonded to a rigid material base is considered by employing the Gurtin-Murdoch continuum theory of elastic material surfaces. The fundamental solutions corresponding to buried vertical and horizontal line loads are obtained by using Fourier integral transform techniques. Selected numerical results are presented for the cases of a finite elastic layer and a semi-infinite elastic medium to portray the influence of surface elasticity and residual surface stress on the bulk stress field. It is found that the bulk stress field depends significantly on both surface elastic constants and residual surface stress. The consideration of out-of-plane terms of the surface stress yields significantly different solutions compared to previous studies. The solutions presented in this study can be used to examine a variety of practical problems involving nanoscale/soft material systems and to develop boundary integral equations methods for such systems.

키워드

참고문헌

  1. Chen, C.S., Wang, C.K. and Chang, S.W. (2008), "Atomistic simulation and investigation of nanoindentation, contact pressure and nanohardness", Interact. Multiscale Mech., 1(4), 411-422. https://doi.org/10.12989/imm.2008.1.4.411
  2. Chen, J. and Lee, J.D. (2010), "Atomistic analysis of nano/micro biosensors", Interact. Multiscale Mech., 3(2), 111-121. https://doi.org/10.12989/imm.2010.3.2.111
  3. Dingreville, R. and Qu, J. (2007), "A semi-analytical method to compute surface elastic properties", Acta Mater., 55, 141-147. https://doi.org/10.1016/j.actamat.2006.08.007
  4. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Rat. Mech. Anal., 57, 291-323.
  5. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14, 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  6. He, L.H. and Lim, C.W. (2006), "Surface green functions for a soft elastic half-space: influence of surface stress", Int. J. Solids Struct., 43, 132-143. https://doi.org/10.1016/j.ijsolstr.2005.04.026
  7. Huang, G.Y. and Yu, S.W. (2007), "Effect of surface elasticity on the interaction between steps", J. Appl. Mech., 74, 821-823. https://doi.org/10.1115/1.2424473
  8. Intarit, P., Senjuntichai, T. and Rajapakse, R.K.N.D. (2010), "Dislications and internal loading in a semi-infinite elastic medium with surface stresses", Eng. Fracture Mech., 77, 3592-3603. https://doi.org/10.1016/j.engfracmech.2010.04.026
  9. Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11, 139-147. https://doi.org/10.1088/0957-4484/11/3/301
  10. Peters, R.D., Yang, X.M., Wang, Q., de Pablo, J.J. and Nealey, P.F. (2000), "Combining advanced lithographic techniques and self-assembly of thin films of diblock copolymers to produce templates for nanofabrication", J. Vac. Sci. Technol. B, 18, 3530-3534. https://doi.org/10.1116/1.1313572
  11. Piessens, R., Doncker-Kapenga, E., Uberhuber, C.W. and Kahaner, D.K. (1983), QUADPACK: A subroutine package for automatic integration, Springer, Berlin.
  12. Povstenko, Y.Z. (1993), "Theoretical investigation of phenomena caused by heterogeneous surface tension in solids", J. Mech. Phys. Solids, 41, 1499-1514. https://doi.org/10.1016/0022-5096(93)90037-G
  13. Shenoy, V.B. (2005), "Atomistic calculations of elastic properties of metallic fcc crystal surfaces", Phys. Rev. B, 71, 094104. https://doi.org/10.1103/PhysRevB.71.094104
  14. Sneddon, I.N. (1951), Fourier transforms, McGraw-Hill, New York.
  15. Srinivasan, U., Liepmann, D. and Howe, R.T. (2001), "Microstructure to substrate self-assembly using capillary forces", J. Microelectromech. Syst., 10, 17-24. https://doi.org/10.1109/84.911087
  16. Wang, Z.Q., Zhao, Y.P. and Huang, Z.P. (2010), "The effects of surface tension on the elastic properties of nano structures", Int. J. Eng. Sci., 48, 140-150. https://doi.org/10.1016/j.ijengsci.2009.07.007
  17. Wong, E., Sheehan, P.E. and Lieber, C.M. (1997), "Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes", Science, 277, 1971-1975. https://doi.org/10.1126/science.277.5334.1971
  18. Yakobson, B.I., Nanomechanics, In: Goddard, W.A., Brenner, D.W., Lyshevsk, S.E. and Iafrate, G.J. editors. (2003), Handbook of nanoscience, engineering and technology, CRC Press, Boca Raton.
  19. Zhao, X.J. and Rajapakse R.K.N.D. (2009) "Analytical solutions for a surface-loaded isotropic elastic layer with surface energy effects", Int. J. Eng. Sci., 47, 1433-1444. https://doi.org/10.1016/j.ijengsci.2008.12.013

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