Modelling planar kirigami metamaterials as generalized elastic continua. (26th April 2023)

• Record Type: Journal Article
• Authors: Zheng, Y.; Niloy, I.; Tobasco, I.; Celli, P.; Plucinsky, P.
• Is Part Of: Proceedings. Volume 479:Number 2272(2023)
• Publication Date: 2023-04-26
• Subjects: metamaterials -- kirigami -- continuum modelling -- finite-element method; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2022.0665
• Languages: English
• ISSNs: 1364-5021

Abstract

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.