Static Bending Analysis of Nanobeam-Substrate Medium Systems Incorporating Mixture Stress-Driven Nonlocality, Surface Energy, and Substrate-Structure Interactions

This paper proposes a novel nonlocal beam-substrate model for the static bending analysis of a nanobeam system on a substrate medium. The proposed model incorporates the coupling interaction among nonlocality, surface energy, and substrate-structure interaction. The mixture stress-driven nonlocal model is used to capture the material’s small-scale effects inherent in micro- and nanoscale systems, resulting in well-posed micro- and nanostructure responses. The Gurtin-Murdoch continuum surface-energy model and the Winkler foundation model, which respectively represent size-dependent and substrate-structure interaction effects, are considered. The governing differential equation (GDE) and its relevant boundary conditions are derived based on the displacement-based principle. The analytical solutions are directly obtained from the GDE and employed to assess the bending responses. To demonstrate the impact of the mixture parameter, surface energy, and substrate-structure interaction on the static bending analysis of nanobeam systems, four numerical simulations are conducted. The first simulation validates the proposed nanobeam system by comparing it to experimental results, while the second simulation demonstrates the impact of surface energy and substrate-structure interaction on beam deflection. The third and fourth simulations analyze the impact of different system variables on the normalized transverse displacement and effective bulk Young's modulus (EBYM), respectively. The analysis results demonstrate that material nonlocality caused by the mixture parameter and length-scale parameter, as well as surface energy and substrate-structure interaction effects, impact the bending behaviors of the nanobeam systems.