Analysis of Out-of-Plane Deformation of Kirigami Structure using Beam Deformation Theory

We constructed a theoretical model describing the relationship between tensile force and the angle of out-of-plane deformation in a kirigami structure to enable quantitative geometric design. While kirigami structures are promising for stretchable electronics, existing design methods often rely heavily on simulations, making inverse design difficult. In this study, we analyzed the three-dimensional static deformation of a kirigami structure. The mechanism was modeled as a combination of a both-ends-fixed beam within the kirigami structure and a cantilever between the kirigami unit and the connecting frame. Our analysis revealed that the deformation of the internal fixed-fixed beam predominantly governs the out-of-plane deformation. The derived analytical expression, which incorporates key dimensional parameters, showed good agreement with the experimental results. This method offers an efficient pathway for the geometrical design of kirigami structures with target mechanical properties.