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Journal of Nanomaterials
Volume 2013 (2013), Article ID 635428, 14 pages
Research Article

Modeling of Axially Loaded Nanowires Embedded in Elastic Substrate Media with Inclusion of Nonlocal and Surface Effects

1Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand
2Civil Engineering Program, School of Engineering, University of Phayao, Phayao 56000, Thailand

Received 12 July 2013; Accepted 2 August 2013

Academic Editor: Chunyi Zhi

Copyright © 2013 Suchart Limkatanyu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlocal and surface effects are incorporated into a bar-elastic substrate element to account for small-scale and size-dependent effects on axial responses of nanowires embedded in elastic substrate media. The virtual displacement principle, employed to consistently derive the governing differential equation as well as the boundary conditions, forms the core of the displacement-based finite element formulation of the nanowire-elastic substrate element. The element displacement shape functions, analytically derived based on homogeneous solution to the governing differential equilibrium equation of the problem, result in the exact element stiffness matrix and equivalent load vector. Two numerical simulations employing the proposed model are performed to study characteristics and behavior of the nanowire-substrate system. The first simulation involves investigation of responses of the wire embedded in elastic substrate. The second examines influences of several system parameters on the contact stiffness and reveals the size-dependent effect on the effective Young's modulus of the system.