Size effects in micro/nanostructures: a review of mechanical theories and modeling

(Figure presented.) Micro/nanostructures exhibit distinctive mechanical, thermal, and electrical properties due to their unique size effects, significantly differentiating them from bulk materials. This paper offers a comprehensive review of theoretical and simulation advancements in the mechanical performance of micro/nanostructures, specifically accounting for these size effects. The discussion begins by analyzing the physical mechanisms underlying surface and small-size effects, along with their impacts on material properties, as evidenced by experimental observations. Then, the development of non-classical continuum theories is reviewed, including nonlocal elasticity, couple stress theory, strain gradient theory, and surface elasticity theory. A detailed analysis is provided of their respective advantages and limitations in accurately capturing mechanical behavior at the micro/nanoscale. Furthermore, the role of numerical simulation methods, such as molecular dynamics, finite element analysis, and multiscale techniques, in investigating the underlying mechanisms of micro/nanostructures is explored. Representative case studies, such as nanoindentation and microbeam bending, are presented to illustrate the applicability and challenges of each method. The mechanical properties and size effects of micro/nanolattice structures are also highlighted, demonstrating their potential for lightweight and high-strength material applications. Finally, a concise outlook on future research directions regarding size effects in micro/nanostructures is provided, suggesting promising new mechanisms and avenues for further exploration.