Abstract
Kirigami, as a scientific concept that emerges with but distinguishes from origami, provides a unique paradigm for engineering mechanical properties of a surface through geometric analysis. Cutting geometry that enables panel rotations around shared nodes—by itself or in conjunction with folding geometry that allows panel rotations around shared edges—yields predictable mechanical responses ranging from two-dimensional to three-dimensional deformations and from shape-fitting to metamaterial functionalities. This contribution reviews the deterministic relationships between geometry of a kirigami surface and its mechanical responses under given external loading. We highlight rigid or non-rigid two-dimensional deformations determined by the convexity, compatibility, or symmetry of the cutting patterns (e.g., tessellations characterized by wallpaper groups); three-dimensional deformations controlled by cutting distance versus surface thickness, slit shapes, or the combined effect of cuts and folds; and mechanical metamaterial functionalities arising from unique lattice connections and panel orientations, including topological polarization transformation, static non-reciprocity, and Poisson?s ratio functional variation. We address various methodologies for linking geometry and mechanics in kirigami surfaces, including theoretical analyses, surrogate modeling or finite element simulations, and experimental evaluations. We also discuss strategies for fabricating kirigami surfaces, such as 3D printing, molding, assembling, cutting, and folding. Finally, we project a vision for the field of kirigami engineering by emphasizing the mechanisms that transform subtle geometric characteristics of kirigami surfaces into their unique mechanical properties.
