Abstract
A theory of kirigami's high-extensibility transition shows a striking analogy with Landau theory of continuous transitions, if a rotation angle and elongation of kirigami are regarded as the order parameter and the inverse temperature.
Highlights
Kirigami’s high extensibility has been understood as a transition in the force-elongation curve
In our recent work [21], we showed that our previous model proposed in Ref. [8] predicts a discontinuous transition and the prediction on the ratio between the forces just before and after the jump agrees semiquantitatively with experimental data obtained from kirigami samples made of Kent paper
The energy obtained above behaves as the Landau free energy for the second-order transition, if we identify θ as the order parameter and δ as the inverse temperature
Summary
Continuity and discontinuity of kirigami’s high-extensibility transition: A statistical-physics viewpoint. Kirigami’s high extensibility has been understood as a transition in the force-elongation curve In this Rapid Communication, we consider a model, which modifies our previous model, to show a striking analogy between the present theory and the Landau theory of continuous thermodynamic transitions, if we regard a rotation angle and elongation of kirigami as the order parameter and the inverse temperature, respectively. The high stretchability of the basic kirigami structure [see Fig. 1(a)] has been explained by a simple model based on bending energy [8] This transition manifests as a transition in the force-elongation curve. We generalize our previous model and show that the kirigami’s high-extensibility transition can be physically identified with the Landau theory of the second-order transition [22,23], if we regard a rotation angle θ and elongation δ of each unit as the order parameter and the inverse temperature, respectively. In the in-plane deformation, the central part of volume hwd of the (2n − 1)th (2nth) elementary unit
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