Harnessing disorder to decouple extension and shear in kirigami metamaterials

Abstract

Kirigami transforms stiff sheets into compliant, shape-morphing structures via periodic cut patterns. These repeating motifs rotate with stretch, so that extension in general leads to shear, and anisotropic properties cannot be tuned independently. Biological tissues evade this through controlled disorder, such as graded fiber orientations in skin and hierarchical anisotropy in myocardium. Here, we show that engineered disorder is tunable design degree of freedom: stochastic kirigami accesses a continuous and far broader region of mechanical response than periodic patterns, including programmable anisotropy with near-complete suppression of extension–shear coupling. Because disordered patterns lack a simple parameterization, we navigate this space with a geometry-aware graph neural network (GNN) that maps cut topology to full nonlinear, bidirectional stress–strain response, coupled to a genetic algorithm for inverse design of kirigami patterns that reproduce target stress–strain responses in two perpendicular loading directions. The GNN is trained an order of magnitude faster and more accurately than image-based models. Fabricated elastomer samples reproduce the targeted nonlinear, anisotropic responses, closing the loop from design to physical component. By turning disorder into a control axis for directional stiffness, this work points toward architected materials that stretch without parasitic shear, enabling tissue-interfacing devices matched to the anisotropy of living tissue.