# Continuity and discontinuity of kirigami's high-extensibility transition: a statistical-physics viewpoint

## TL;DR

This paper models kirigami's high-extensibility transition using statistical physics, revealing a analogy with thermodynamic phase transitions and emphasizing the importance of transition continuity in mechanical response.

## Contribution

It introduces a modified model linking kirigami's extensibility transition to Landau theory, highlighting the role of transition nature in mechanical behavior.

## Key findings

- The transition can be continuous or discontinuous, affecting mechanical response.
- A theoretical analogy with thermodynamic phase transitions is established.
- The model provides a new framework for understanding kirigami mechanics.

## Abstract

Recently, kirigami's high extensibility has been understood as a transition in the force-elongation curve. In this paper, we consider a model, which modifies our previous model, to show a striking analogy between the present theory and 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 present study opens a new avenue in physics, pointing out the importance of the distinction between discontinuity and continuity of the high-extensibility transition in an elementary kirigami structure, and showing that the mechanical response of kirigami can be understood using the tools of statistical physics, which have been proved to be useful in many fields of physics.