Molecular Dynamics Benchmarks for Size-Dependent Tension, Bending, Buckling, and Vibration of Nanobeams

Nonclassical continuum mechanics-based modeling of small-scale structures, such as micro- or nanobeams, is a prominent research topic that has been extensively investigated and is also beneficial for designing small-scale intelligent devices. The accuracy of size-dependent beam models remains untested in many instances within the literature due to the scarcity of experimental and molecular dynamics (MD) results at small scales. This paper aims to provide comprehensive MD benchmark solutions that facilitate verifying 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 or rectangular cross-sections. The size effects that arise from the scaling effect (where all dimensions of the nanobeams change proportionally) and variations in thickness and length are systematically studied. The findings demonstrate that the size effect depends on the type of mechanical problem and the aspect ratio of the nanobeams. In all cases, the silicon nanobeams demonstrate a softer mechanical response as their dimensions decrease.