13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 10 12 14 16 18 20 22 24 26 28 30 2 3 4 5 6 7 8 9 10 11 12 w p w p w p ˆ ˆ C =30,C =3 ˆ ˆ C =30,C =0 ˆ ˆ C =0,C =0 L/D Figure 2. Variation of the normalized critical buckling force of a simply supported NW lying on Winkler-Pasternak substrate medium with respect to its aspect ratio. The diameter of the NW is3.5nm. 4. Conclusions In this paper, the Steigmann-Ogden model is adopted to characterize the surface effect of the NW. Explicit solutions are obtained for the critical buckling force and buckling mode of a simply supported NW lying on Winkler-Pasternak substrate medium with the Timoshenko beam theory. The following conclusions are drawn through this study: (1) The shear effect, the surface stress effect and curvature dependent surface energy all have influences on the critical buckling force of the NW. The importance of these influences is highly dependent on the diameter and aspect ratio of the NW. (2) The Steigmann-Ogden correction can stiffen or soften the NW, depending on the sign of the Steigmann-Ogden constant. (3) Both the Winkler modulus and Pasternak modulus tend to stiffen the NW. The critical buckling force of the NW is more sensitive to the Pasternak modulus. Acknowledgement The support of National Natural Science Foundation of China under contract No. 10802032 is most sincerely appreciated. References [1] M.E. Gurtin and A.I. Murdoch, A continuum theory of elastic material surfaces. Arch Ration Mech Anal, 57 (1975) 291–323. [2] M.E. Gurtin and A.I. Murdoch, Surface stress in solids. Int J Solids Struct., 14 (1978) 431–440. [3] P. Sharma, S. Ganti, N. Bhate, Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl Phys Lett, 82 (2003) 535–537. [4] G.F. Wang and X.Q. Feng, Surface effects on buckling of nanowires under uniaxial compression. Appl Phys Lett, 94 (2009) 141913–1419133.
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