Continuum field theory for the deformations of planar kirigami

Abstract

Mechanical metamaterials exhibit exotic properties at the system level, that emerge from the interactions of many nearly rigid building blocks. Determining these emergent properties theoretically has remained an open challenge outside of a few select examples. Here, for a large class of periodic and planar kirigami, we provide a coarse-graining rule linking the design of the panels and slits to the kirigami's macroscale deformations. The procedure gives a system of nonlinear partial differential equations (PDE) expressing geometric compatibility of angle functions related to the motion of individual slits. Leveraging known solutions of the PDE, we present excellent agreement between simulations and experiments across kirigami designs. The results reveal a surprising nonlinear wave-type response persisting even at large boundary loads, the existence of which is determined completely by the Poisson's ratio of the unit cell.

5 pages, 4 Figures and a supplement

References in corpus (6)

• Programming Curvature using Origami Tessellations
• Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
• Buckling-Induced Kirigami
• Kirigami Actuators
• Conformal Elasticity of Mechanism-Based Metamaterials
• Theorem on the Compatibility of Spherical Kirigami Tessellations

Cited by in corpus (15)

• Conformal Elasticity of Mechanism-Based Metamaterials
• An additive framework for kirigami design
• Strain compatibility and gradient elasticity in morphing origami metamaterials
• Modelling planar kirigami metamaterials as generalized elastic continua
• Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial
• Programming bistability in geometrically perturbed mechanical metamaterials
• Some results on the Guest-Hutchinson modes and periodic mechanisms of the Kagome lattice metamaterial
• Polymer networks which locally rotate to accommodate stresses, torques, and deformation
• Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
• Asymptotic, second-order homogenization of linear elastic beam networks
• Tailoring asymmetry for anisotropic friction in kirigami metamaterial skins with pop-up folding hinges
• Curvature screening in draped mechanical metamaterial sheet
• Lagrangian approach to origami vertex analysis: Kinematics
• Tunable Topological Phases in Quantum Kirigamis
• Reinforcement learning for inverse structural design and rapid laser cutting of kirigami prototypes