Modelling planar kirigami metamaterials as generalized elastic continua

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.

References in corpus (8)

• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• Conformal Elasticity of Mechanism-Based Metamaterials
• Compact reconfigurable kirigami
• Continuum field theory for the deformations of planar kirigami
• Microtwist elasticity: A continuum approach to zero modes and topological polarization in Kagome lattices
• Theorem on the Compatibility of Spherical Kirigami Tessellations
• Strain compatibility and gradient elasticity in morphing origami metamaterials
• Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors

Cited by in corpus (5)

• Automated discovery of reprogrammable nonlinear dynamic metamaterials
• Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial
• Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
• Curvature screening in draped mechanical metamaterial sheet
• Lagrangian approach to origami vertex analysis: Kinematics