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| Analytical model of micro/nano-cylinders considering Steigmann-Ogden surface effect |
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Abstract Due to a sharp increase of surface-to-volume ratio of nano-sized cylindrical subjects, the corresponding surface energy becomes significant. Therefore, it is essential to study the surface effect at the nano-scale. Herein we study the elastic response of nano-cylinders under diametral loading by taking into account of the Steigmann-Ogden (S-O) surface theory. The S-O surface is assumed as a zero-thickness film attached to a bulk material with bending stiffness and residual surface tension. Relative to the more popular Gurtin-Murdoch (G-M) interface model, S-O surface can resist not only tension but also bending. Based on continuum mechanics theory, the present work develops internal analytical expressions by solving the elastic governing equations through series expansion in cylindrical coordinate. The internal unknown coefficients are finally obtained by applying S-O surface model and extended diametral boundary conditions through mathematical orthogonality. When the surface bending stiffness parameters are ignored, the present results can be degenerated to the G-M model. Finite element simulations and experimental measurements in the literature are employed to verify the present theory with good agreement. Based on the credence of present solutions, the effects of surface bending stiffness parameters, surface residual stress and cylinder dimension are investigated and discussed on material properties of nano-cylinders. The results demonstrate that the S-O model generates different stress distributions relative to the G-M model, indicating that the surface bending stiffness parameters can not be ignored in the nano-scale. In addition, the surface residual stress plays a certain role in influencing the stress distributions of both solid and hollow nano-cylinders, especially on the surface of hollow ones. What’s more, it is found that the surface effect gradually increases with a decrease of the cylinder’s dimension. Finally, the analytical nature of the present solution offers attractive alternative to the numerical methods in studying elastic behavior and surface effects of nano-subjects.
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Received: 19 May 2021
Published: 19 April 2022
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2022, Vol. 43 
