Tension-induced Buckling with Dual Stiffness in Square-wave Thin Sheets

This work reveals a tension-induced out-of-plane buckling mechanism in square-wave thin sheets, which exhibit distinctly different pre-buckling and post-buckling stiffness. Simplified theoretical analysis identifies that bending of the transverse beams about their weak axis is the dominant mode, while the torsional critical load is substantially higher. Based on this bending-dominated mechanism, analytical solutions for the critical buckling load and dual stiffness are derived and validated through finite element simulations. In the post-buckling regime, the structure maintains a stable load-carrying capacity despite the reduced stiffness. For series-connected arrays, the critical buckling load is found to be independent of the number of periods, whereas both pre- and post-buckling tensile stiffness scale inversely with the period count. When extended to orthogonal mesh structures, the supporting link length exhibits a non-monotonic effect on the critical load: increasing the link length initially raises the critical load, but beyond a threshold, bending of the links themselves weakens the constraint and reduces the load. This mechanism is further confirmed by comparative simulations with rigid links, where the non-monotonicity disappears and the critical load monotonically increases with length. These results collectively demonstrate that the stiffness transition from high to low with displacement provides a natural threshold-triggered switching mechanism. Quantitatively, the ratio of pre- to post-buckling stiffness exceeds an order of magnitude, demonstrating a pronounced switching capability. Overall, this work not only deepens the fundamental understanding of tensile buckling in periodic thin-walled structures but also provides explicit theoretical foundations and design guidelines for threshold-triggered sensors, impact recorders, soft robotics, and mechanical metamaterials.