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Buckling of nanowires: a continuum model with a transition parameter

In this work, a continuum model with a transition parameter for the buckling of nanowires is presented. The present model is developed by means of the principle of virtual displacement within the framework of continuum mechanics. A transition parameter characterizing the directions of the axial loads on the cross sections of buckled nanowires is introduced. The critical buckling loads (CBLs) of the nanowires with simply supported, clamped-clamped and clamped-free end conditions are derived from the present model. The present model is validated via comparisons with the results available in the literature. Numerical results reveal that the transition parameter plays an important role in the determination of CBLs, which is related to the end conditions and cross-sectional shapes of nanowires. The differences in the magnitudes of CBLs corresponding to two extreme values of the transition parameter may reach up to 13.8% for clamped-clamped nanowires. The comparison between the CBLs from the present model and molecular dynamics simulation shows that the present model may predict more reliable CBLs than the existing continuum models do. The present solutions could therefore serve as the benchmarks with the lower and upper bounds. The modeling methodology in this work holds a promise for the theoretical study on the buckling of nanotubes and nanoplates.