13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- The buckling force of the NW is normalized with the critical buckling force of a classic simply supported Euler-Bernoulli beam. To see qualitatively how the surface stress effect and the Steigmann-Ogden correction influence the buckling behavior of the NW, we adopt the following material parameters in this study: 76Gpa E , 0.3 , 0 0.65 N/m , 0 1.39N/m C , 1 153.6eV C . In Figure 1., we ignore the transverse shear effect of the substrate. The diameter and Steigmann-Ogden constant are chosen to be 3.5nmand 153.6eVrespectively. All the results are normalized with the critical buckling force of a classic simply supported Euler-Bernoulli beam at each aspect ratio. Figure 1. shows that the surface effect has significant influences on the normalized critical buckling forces. When the Steigmann-Ogden constant is positive, the critical buckling force is greater than that predicted by the Gurtin-Murdoch theory, which implies that the NW is stiffened. It is also noted that the influence of the surface effect (predicted either by the Gurtin-Murdoch model or the Steigmann-Ogden model) on the critical buckling force decreases when the diameter of the NW increases. The difference between the result predicted by the Gurtin-Murdoch theory and that by the Steigmann-Ogden theory is also largely decreased as the diameter of the NW increases. Fig. 1 also shows that the critical buckling force for a finitely long NW is always larger than that for an infinitely long NW. 10 12 14 16 18 20 22 24 26 28 30 1 2 3 4 5 6 7 8 9 10 11 L/D an infinite nanowire with curvature-dependent surface energy a finite nanowire with curvature-dependent surface energy a classical Timoshenko beam of infinite length a classical Timoshenko beam of finite length an infinite nanowire based on the Gurtin-Murdoch theory a finite nanowire based on the Gurtin-Murdoch theory Figure 1. The normalized critical buckling force of a simply support NW lying on Winkler substrate medium. In Figure 2., the influences of the Winkler and Pasternak moduli on the critical buckling force are studied with the Timoshenko beam model. The material parameters are the same with those in Figure 1.. The diameter of the NW is set to3.5nm. From Figure 2., we find that both the Winkler modulus and the Pasternak modulus tend to stiffen the NW. As a result, the buckling force for a NW lying on substrate medium is always larger than that of a free NW. It is also noticed that the critical buckling force is more sensitive to the Pasternak modulus.
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