Bending response of tape springs against a notched indenter

In recent years, the mechanics of shells have been studied experimentally and theoretically, both from fundamental and engineering points of view. Especially, the cylindrical shells deform flexibly despite their high rigidity. The rigidity of cylindrical shells plays an important role in designing industrial products or even in the mechanical functionality of living organisms. Geometrically nonlinear response of shells is observed when we bend an open cylindrical shell or a tape spring. Upon small deformation, the tape spring bends uniformly. When the applied moment (or indenting force on three-point bending) reaches the critical value, the bending deformation is localized and then the tape spring snaps. Despite the number of studies on the mechanical performance of tape springs, the effects of the geometry of indenters have not been clarified so far. Here, we perform a three-point bending test for tape springs, using the indenters of different-shaped caps to uncover their roles. We find that the curvature of the indenter plays a central role in critical snap-buckling load. The change in their mechanical performance originates from the subtle interplay of elasticity and geometry.