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.

Keywords: flexible device; kirigami structure; mechanical metamaterials; stretchable electronic substrate.

Figure 1

Parameters of a kirigami structure and cut patterns.

Figure 2

(a) Photograph of a stretched kirigami structure. (b) Definition of non-uniform deformed regions at both ends. (c) A spring model of the kirigami structure, in which two hard springs with an elongation stress per strain E₀(ε₀) sandwich n − 2 soft springs with an elongation stress per strain E₁(ε₁). (d) The combined stress–strain curve of the whole spring σ_c(ε) can be obtained from stress–strain curves σ₀(ε) and σ₁(ε) of each spring.

Figure 3

(a) Photograph of the tensile test setup, and (b) definition of the test piece shape in the tensile test and parameter dimensions.

Figure 4

Stress–strain diagram when stretching the kirigami structure for different values of n.

Figure 5

Comparison between fitting curve by theoretical and measured values: (a) Relation between n and elongation stress per strain, (b) Relationship between n and breaking strain.

Figure 6

Comparison of values calculated using the spring model and values in the stress–strain diagram from the tensile test for n = 10 using the test piece.