Snapping-back buckling of wide hyperelastic columns

Abstract The mechanical instability of columns with a low width-to-length ratio under axial compression has been studied for more than 260 years, known as the Euler buckling. Such columns buckle at a critical strain on the order of 1%, after which the compressive load continuously increases with the displacement. Recently, in the advance of soft robotics and mechanical metamaterials, researchers have harnessed buckling of high width-to-length ratio columns to achieve new functions. However, buckling and post-buckling of these columns are not well studied. Here we show hyperelastic columns, depending on their width-to-length ratio, can undergo continuous, snapping-through, or snapping-back buckling. In particular, we identify a new snapping-back mode of column buckling, in which beyond the onset of buckling, a column bends to form a sub-critical crease. Our analytical discrete model reveals that snapping-back buckling results from strong coupling between stretching and bending. A phase diagram is constructed to demarcate the different buckling modes of axially compressed columns.