13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Buckling Analysis of a Nanowire Lying on Winkler-Pasternak Elastic Foundation Tiankai Zhao1, Jun Luo1,* 1 Department of Mechanics , Huazhong University of Science and Technology, Wuhan 430074, China * Corresponding author: luojun.l@gmail.com Abstract The Steigmann-ogden surface elasticity model and the Timoshenko beam theory are adopted to study the axial buckling of a nanowire (NW) lying on Winkler-Pasternak substrate medium. Explicit solutions of the critical buckling force and buckling mode are obtained analytically. The influences of the surface stress effect, the geometry of the NW and the elastic foundation moduli are systematically discussed. Keywords Surface effect, Nanowire, Timoshenko beam theory, Buckling 1. Introduction Nanowire (NW) based devices have found important applications in various fields. Traditional beams theories failed to interpret the size dependent mechanical behavior of these devices due to their surface stress effect. The Gurtin-Murdoch model [1-2] has been widely accepted to study the mechanical behavior of nanostructures and nano defects [3-7]. Some researchers found that the effective elastic moduli of nanostructures under bending and tension are different[8-9], which could not be explained by the Gurtin-Murdoch model. Chhapadia et al.[10] pointed out that the above discrepancy could be explained with the modified framework proposed by Steigmann and Ogden [11-12]. On the other hand, buckling has long been thought as an unwanted issue and should be strictly avoided in structural designs. However, it was demonstrated by some researchers that controlled buckling of slender structures such as thin films, nanowires and nanotubes on compliant substrates could be utilized in the design of flexible electronics. This paper aims to study the axial buckling of a simply supported NW lying on Winkler-Pasternak elastic foundation with the Timoshenko beam model and Steigmann–Ogden theory. The influences of the surface stress effect, the geometry of the NW and the elastic foundation moduli are systematically discussed. 2. Solution of the Problem Consider a NW lying on a deformable substrate, which is subjected to distributed transverse load and axial forces at both ends. We assume the NW has a circular cross section. The total energy of the axially loaded nanobeam can be written as: ( ) ( ) ( ) Total Bulk Surface U w U w U w , (1) where: 2 2 0 0 1 ( ) ( ) ( ) 2 2 L L Bulk A A w U w E y dAdx G dAdx x x , (2) 2 2 2 0 0 1 2 0 1 1 ( ) [ ( ) ( ) ] 2 2 L Surface S w U w y C y C dSdx x x x . (3)
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