A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

This paper presents a bar-elastic substrate model to investigate the axial responses of nanowire-elastic substrate systems considering the effects of nonlocality and surface energy. The thermodynamics-based strain gradient model is adopted to capture the nonlocality of the bar-bulk material while the Gurtin-Murdoch surface theory is utilized to consider the surface energy. To characterize the bar-surrounding substrate interaction, the Winkler foundation model is employed. In a direct manner, system compatibility conditions are obtained while within the framework of the virtual displacement principle, the system equilibrium condition and the corresponding natural boundary conditions are consistently obtained. Three numerical simulations are conducted to investigate the characteristics and behaviors of the nanowire-elastic substrate system: the first is conducted to reveal the capability of the proposed model to eliminate the paradoxical behavior inherent to the Eringen nonlocal differential model; the second is employed to characterize responses of the nanowire-elastic substrate system; and the third is aimed at demonstrating the dependence of the system effective Young's modulus on several system parameters.