Mechanism-based metamaterials with microstructurally invariant shape-change

Abstract

Metamaterials with low-energy 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.

Figures (4)

• Figure 1: Metamaterials with counter-rotating mechanisms: (a) the RS pattern; (b) a generalization constructed from our design recipe. The unit cell of each pattern is emphasized.
• Figure 2: (a-e) Recipe to create 2D mechanism-based metamaterials of arbitrary topology. (a) Start with a plane tiling. (b) Separate the panels through a tensor $\mathbf{D}$. (c) Add new panels to produce the overall pattern. (d) The panels counter-rotate under a mechanism deformation; (e) the slits actuate through angle $\xi$. (f-h) Notation for deriving the effective shape-change of the mechanism motion. (f) Unit cell of the plain tiling and (g) of the metamaterial before deformation. (h) Illustration of how the transformation $\mathbf{D}$ introduces a new set of edge vectors. (i) Unit cell of the metamaterial after deformation.
• Figure 3: Programming kinematics and elasticity in examples. (a) Effective stretch diagram for conformal kirigami (blue) and neutral Poisson's ratio kirigami (red). (b-c) A structured and unstructured example of conformal kirigami; the undeformed and most actuated states are shown. (d-e) Analogous structured and unstructured examples for neutral Poisson's ratio kirigami. (f) Kinematic validation --- the experimental data markers are overlaid onto the full range of theoretical actuation; the data points are obtained using the procedure in SM.3.B suppl. (g) Conformal kirigami with identical shape-change and tension springs connecting the panels' centroids. (h) Elastic energy of the metamaterials in (g) as a function of the actuation angle.
• Figure 4: Generalizations. (a) Compact 2D kirigami; (b) non-planar kirigami; (c) 3D metamaterials.