Modelling planar kirigami metamaterials as generalized elastic continua

TL;DR

This paper develops a generalized continuum model for planar kirigami metamaterials, accurately predicting their nonlinear deformation response under various loads by integrating local mechanisms, slit actuation, and hinge bending effects.

Contribution

It introduces a novel finite-element-based continuum model that captures the complex nonlinear behavior of kirigami metamaterials at engineering scales.

Findings

Model predictions match experimental results quantitatively.

The model effectively captures the nonlinear deformation mechanisms.

Simulations are consistent across different designs and load conditions.

Abstract

Kirigami metamaterials dramatically change their shape through a coordinated motion of nearly rigid panels and flexible slits. Here, we study a model system for mechanism-based planar kirigami featuring periodic patterns of quadrilateral panels and rhombi slits, with the goal of predicting their engineering scale response to a broad range of loads. We develop a generalized continuum model based on the kirigami's effective (cell-averaged) nonlinear deformation, along with its slit actuation and gradients thereof. The model accounts for three sources of elasticity: a strong preference for the effective fields to match those of a local mechanism, inter-panel stresses arising from gradients in slit actuation, and distributed hinge bending. We provide a finite-element formulation of this model and implement it using the commercial software Abaqus. Simulations of the model agree quantitatively with experiments across designs and loading conditions.