Unbuckling of superelastic shape memory alloy columns

Abstract

Our recent buckling experiments on superelastic shape memory alloy columns (initially straight rods and tubes) discovered that during axial shortening, certain specimens bent (buckled) at a critical compressive load and then, surprisingly, straightened (unbuckled) at a larger compressive load. This “buckling–unbuckling” phenomenon, defined here as the deviation from and then return to a straight configuration during monotonic loading, is not only an intriguing phenomenon (contrary to the post-buckling behavior of conventional materials) but also presents the possibility for novel applications. This work aims to provide a clearer understanding of when and why unbuckling occurs, presenting the experimental observations of this phenomenon and the stability analysis of a modified Shanley column model that captures the unbuckling behavior. Unbuckling behavior is shown to be a consequence of a secondary branch that deviates from the principal path at a low-load level (critical buckling load), but reattaches to the principal path at a higher load level (unbuckling load). The analysis shows that unbuckling behavior can only occur for certain combinations of column geometries and nonlinear (stiff–soft–stiff) material laws, that is, relatively stout columns with the right sequence of softening/stiffening to create the necessary restorative bending moment to reset the column to a straight configuration. The feasible space is defined by closed-form bounds on geometric and material parameters, along with a sensitivity analysis of these parameters on the amplitude of unbuckling.