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

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