Mechanism-based metamaterials with microstructurally invariant shape-change

Metamaterials with floppy modes called mechanisms are a burgeoning template for shape-morphing systems and structures across scales. Here, we present a design recipe that transforms an arbitrary plane tiling into a 2D kirigami pattern with a single degree-of-freedom mechanism motion, greatly expanding the known library of mechanism-based designs. We reveal that these kirigami patterns, when deformed along their mechanism, have a bulk shape change invariant to the underlying microstructure of the pattern. Experimental observations confirm this unusual kinematic prediction in illustrative classes of designs. We also exploit this invariance to elicit different elastic responses in patterns with identical bulk shape change. Finally, we discuss generalizations to compact and non-planar kirigami, as well as 3D metamaterials, highlighting the broad applicability of our new approach to design.