A Simplified Model for Buckling and Post-Buckling Analysis of Cu Nanobeam Under Compression

Both of Buckling and post-buckling are fundamental problems of geometric nonlinearity in solid mechanics. With the rapid development of nanotechnology in recent years, buckling behaviors in nanobeams receive more attention due to its applications in sensors, actuators, transistors, probes, and resonators in nanoelectromechanical systems (NEMS) and biotechnology. In this work, buckling and post-buckling of copper nanobeam under uniaxial compression are investigated with theoretical analysis and atomistic simulations. Different cross sections are explored for the consideration of surface effects. To avoid complicated high order buckling modes, a stress-based simplified model is proposed to analyze the critical strain for buckling, maximum deflection, and nominal failure strain for post-buckling. Surface effects should be considered regarding critical buckling strain and the maximum post-buckling deflection. The critical strain increases with increasing nanobeam cross section, while the maximum deflection increases with increasing loading strain but stays nearly the same for different cross sections, and the underlying mechanisms are revealed by our model. The maximum deflection is also influenced by surface effects. The nominal failure strains are captured by our simulations, and they are in good agreement with the simplified model. Our results can be used for helping design strain gauge sensors and nanodevices with self-detecting ability.