On local kirigami mechanics II: Stretchable creased solutions

TL;DR

This paper models the mechanics of kirigami's fundamental e-cone structure using a discretely creased annular disk, enabling analysis of both inextensible and extensible configurations and their post-buckling behaviors.

Contribution

It introduces a novel creased mechanism model that captures bending and stretching deformations, allowing study of e-cone mechanics beyond the isometric limit.

Findings

Model captures both bending and stretching deformations.

Enables analysis of post-buckling and buckling instabilities.

Provides a fundamental understanding of kirigami phenomenology.

Abstract

Following on Part I of this work series on local kirigami mechanics, we present a study of a discretely creased mechanism as a model to investigate the mechanics of the basic geometric building block of kirigami--the e-cone. We consider an annular disk with a single radial slit discritised by a series of radial creases connecting kinematically flat rigid panels. The creases allow both relative rotation and separation between panels, capturing both bending and stretching deformations. Admissible equilibrium configurations are obtained by penalising these deformations using elastic springs with stiffnesses derived from compatible continuum plate deformations. This provides a tool to study both inextensible and extensible e-cone configurations due to opening of the slit and rotation of its lips. This creased model hence offers the possibility to study the e-cone away from its isometric limit, i.e., for plates with finite thickness, and explore the full range of post-buckling (far-from-threshold) behaviour as well as initial buckling (near-threshold) instability. Our local approach provides a fundamental understanding of kirigami phenomenology, underpinned by a proper theoretical approach to geometry and mechanics.