Design of Rigidity and Breaking Strain for a Kirigami Structure with Non-Uniform Deformed Regions

Abstract

We modeled a kirigami structure by considering the influence of non-uniform deforming cuts in order to theoretically design the mechanical characteristics of the structure. It is known that the end regions of kirigami structures are non-uniformly deformed when stretched, because the deformation is inhibited at the regions close to both the ends connected to the uncut region in the longitudinal direction. The non-uniform deformation affects the overall mechanical characteristics of the structure. Our model was intended to elucidate how cuts at both ends influence these characteristics. We focused on the difference in the deformation degree caused by a cut between the regions close to the ends and the center of the stretched kirigami device. We proposed a model comprising of connected springs in series with different rigidities in the regions close to the ends and the center. The spring model showed good prediction tendency with regard to the curve of the stress–strain diagram obtained using the tensile test with a test piece. Therefore, the results show that it is possible to theoretically design the mechanical characteristics of a kirigami structure, and that such a design can well predict the influence of cuts, which induce non-uniform deformation at both ends.

Engineering by Cuts: How Kirigami Principle Enables Unique Mechanical Properties and Functionalities

“…[87] Another unique design feature is the nonuniform cutting pattern, which is particularly useful to mitigate undesirable boundary effects. [88] If the kirigami sheet with a uniform cut pattern is fully fixed at both ends during stretching, its deformation at the boundary is constrained by the rigid fixtures. Taniyama et al addressed this issue by introducing non-uniform cut patterns-using progressively more trapezoidal facet shapes near the boundaries and adding separation cuts-to increase the stretchability (Figure 5e).…”

Design of a Kirigami Structure with a Large Uniform Deformation Region

“…In recent years, new approaches have been introduced that deal with the structure of substrate materials to achieve stretchable electronic devices [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Among the innovative structures for substrates, kirigami structures with a larger apparent breaking strain than that of the material itself have attracted significant attention [ 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. A kirigami structure is a structure with periodic linear cuts in a substrate.…”

“…Chen et al used FDM to analyze the stress concentration at the edge of a cut with a kirigami structure [ 8 ]. We [ 9 ] modeled a kirigami structure as a series-connected spring. Based on the model, the stiffness of the kirigami structure could be analyzed, considering the non-uniform deformation regions that occurred at both ends during stretching [ 9 ].…”

“…We [ 9 ] modeled a kirigami structure as a series-connected spring. Based on the model, the stiffness of the kirigami structure could be analyzed, considering the non-uniform deformation regions that occurred at both ends during stretching [ 9 ]. Tang et al controlled the inclination direction of the out-of-plane deformation in a kirigami structure by incorporating some of the structures into a kirigami structure [ 10 , 11 ].…”

Editorial for the Special Issue of Selected Papers from the 9th Symposium on Micro-Nano Science and Technology on Micromachines

“…However, the edges of the structures are typically not well constrained and cause instability in the motion. Therefore, a model comprising of connected springs in series with different rigidities in the regions close to the ends and the center is proposed [4]. It showed good agreement with experiments and will contribute to the theoretical design of kirigami structures.…”