Nonlinear deformation of end-supported nanorods based on consistent couple stress and surface elasticity theories - Sitti Prasittikulwat; Jianjun Zhang; Tawich Pulngern; Somchai Chucheepsakul; Boonchai Phungpaingam; Shanqing Xu; Guoxing Lu (Nano Express)
Established findings in nanostructure mechanics have highlighted the limitations of classical continuum theories in predicting mechanical behavior at the nanoscale, particularly for nanostructures like nanorods and nanowires used in nanoelectromechanical systems, sensors, resonators, memory systems, and optical devices. Motivated by these limitations and the need to accurately model both bulk and surface effects, this work aims to integrate two non-classical theories into a unified framework. This study investigates the nonlinear deformation behavior, including large deflection and post-buckling of end-supported nanorods, employing the consistent couple stress theory and surface elasticity theory by Gurtin–Murdoch to account for size-dependent effect and surface effect. A finite element method based on intrinsic coordinates is developed to model the mechanical response of nanorods under various uniform loads and self-weight. The governing equations are derived using a variational approach, incorporating both consistent couple stress and surface elasticity theories to accurately capture the large deflection and post-buckling behavior of nanorods. The Lagrange multiplier method is employed to enforce constrained boundary conditions. Model validation is performed by comparing results with previous research, including experimental, semi-analytical, and numerical approaches, showing strong agreement across various boundary conditions. The study offers a detailed discussion of the distinct roles and applicability ranges of consistent couple stress and surface elasticity theories, highlighting their combined necessity for capturing nanoscale mechanical behavior. Results show that while both consistent couple stress and surface elasticity theories enhance nanorods’ stiffness, the influence of consistent couple stress theory is more dominant, while the relative impact differs under constrained boundary conditions. The findings underscore the importance of including both consistent couple stress and surface elasticity theories in the design and analysis of nanostructures to avoid critical inaccuracies, particularly at high loads where classical continuum theories fail. This work advances predictive modeling capabilities for micro- and nanoscale systems and deepens the understanding of size-dependent mechanics under diverse loading and support conditions, supporting the development of emerging nanotechnologies.