MD benchmarks: Size-dependent tension, bending, buckling, and vibration of nanobeams

H Darban, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 296, 110316 (2025).

DOI: 10.1016/j.ijmecsci.2025.110316

Nonclassical continuum mechanics-based modeling of small-scale structures, such as micro- and nanobeams, is a research topic that has been extensively studied and is beneficial for designing intelligent devices. The accuracy of size-dependent beam models remains unverified in many cases in the literature due to the lack of experimental and molecular dynamics (MD) results at small scales. This paper aims to provide comprehensive MD benchmark solutions that facilitate the verification of nonclassical continuum models for miniaturized beams under tension, bending, buckling, and free transverse vibration. Size- dependent Young's moduli, bending stiffnesses, buckling loads, and natural frequencies are presented through large-scale MD simulations involving up to one million atoms for silicon (Si) nanobeams with square, rectangular, and circular cross-sections. Bending and buckling analyses are conducted on clamped-clamped nanobeams, while a nanocantilever configuration is employed for the vibration analysis. Additionally, novel MD results are presented on the size effect in deflection profiles under bending, as well as buckling and vibrational mode shapes. The size effects resulting from scaling (where all dimensions of the nanobeams change proportionally) and independent variations in thickness, length, and width are systematically investigated. The mechanical problem, aspect ratio, and the cross- sectional geometry of the nanobeams influence the size effect. It is less sensitive to variations in length and weaker in nanobeams with rectangular cross-sections compared to those with circular ones. In all cases, silicon nanobeams exhibit a softer mechanical response as their dimensions decrease, consistent with the size effect previously observed in experiments and atomistic simulations.

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