From continuous to snapping-back buckling: A post-buckling analysis for hyperelastic columns under axial compression

Since Euler's elastica, buckling of straight columns under axial compression has been studied for more than 260 years. A low width-to-length ratio column typically buckles at a critical compressive strain on the order of 1%, after which the compressive load continuously increases with the displacement. Here using a general continuum mechanics-based asymptotic post-buckling analysis in the framework of finite elasticity, we show that a straight hyperelastic column under axial compression exhibits complex buckling behavior. As its width-to-length ratio increases, the column can undergo transitions from continuous buckling, like the Euler buckling, to snapping-through buckling, and eventually to snapping-back buckling. The critical width-to-length ratios for the transitions of buckling modes are determined analytically. The effect of material compressibility on the buckling modes and their transitions is further investigated. Our study provides new insights into column buckling.