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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.

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