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We study, experimentally and theoretically, the mechanical response of sheetmaterials on which line cracks or cuts are arranged in a simple pattern. Suchsheet materials, often called kirigami (the Japanese words, kiri and gami,stand for cut and paper, respectively), demonstrate a unique mechanicalresponse promising for various engineering applications such as stretchablebatteries: kirigami sheets possess a mechanical regime in which sheets arehighly stretchable and very soft compared with the original sheets without linecracks, by virtue of out-of-plane deformation. However, this regime startsafter a transition from an initial stiff regime governed by in-planedeformation. In other words, the softness of the kirigami structure emerges asa result of a transition from the two-dimensional to three-dimensionaldeformation, i.e., from stretching to bending. We clarify the physical originsof the transition and mechanical regimes, which are revealed to be governed bysimple scaling laws. The results could be useful for controlling and designingthe mechanical response of sheet materials including cell sheets for medicalregeneration and relevant to the development of materials with tunablestiffness and mechanical force sensors.

Initial rigid response and softening transition of highly stretchable kirigami sheet materials