Abstract
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.
Highlights
Nowadays, nanotechnology and nanoscience are at the front line of modern research and play a crucial role in developing novel devices and systems at nanoscale
The present work employs two nonclassical elasticity models: the thermodynamics-based strain gradient model and the surface elasticity model to take into account the unique characteristics intrinsic to nano-sized structures
The present work employs this modified strain gradient model formulated within the framework of thermodynamics by Barretta and Marotti de Sciarra [25] to represent the nonlocality of the bar-bulk material
Summary
Nanotechnology and nanoscience are at the front line of modern research and play a crucial role in developing novel devices and systems at nanoscale. Organization of the present work is as follows: brief introductions to thermodynamics-based strain gradient model and surface elasticity model are first described The former is employed to account for small-scale effect while the latter is used to include the size-dependent effect. To study the characteristics and behaviors of the nanowire-elastic substrate system, three numerical simulations employing the proposed model are conducted: the first considering only the small-scale effect is employed to present the capability of the proposed model to eliminate the paradoxical response associated with the Eringen nonlocal differential model; the second is employed to characterize responses of the nanowire-elastic substrate system; and the third is employed to demonstrate the dependence of the system effective Young’s modulus on several system parameters
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