Multimode Ginzburg-Landau Model of a Mesoscopic Euler Strut

An ideal Euler strut has a sequence of buckling instabilities in successively higher-order buckling modes. The higher-mode instabilities are not equilibrium configurations of an ideal strut; they are saddle points of the potential energy functional [1]. They can be stabilized if lower modes are suppressed by constraints, or if mechanical biasing is applied in higher modes. Such biasing may be applied extermally, or it may occur naturally through defects or asymmetry in the bar. We discuss a Ginzburg-Landau model in which the buckling modes comprise the order parameter, the applied compressional strain plays the role of the temperature, and the transverse force profile due to intrinsic asymmetry is analogous to an applied magnetic field. We show how biasing in a higher mode may suppress the instability in the fundamental, and discuss the interpretation of recent experiments on mesoscopic free-standing bars [2]. [1] S. M. Carr, W. E. Lawrence, and M. N. Wybourne, Phys. Rev. B 64 220101(R) (2001). [2] S. M. Carr, W. E. Lawrence, and M. N. Wybourne, APS March Meeting Bulletin (2004).