Arif Abdullah1 K. Jimmy Hsia2

1, Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois, United States
2, Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States

Realization of complex programmable metamaterials where the structural characteristics and functionalities could be tuned beyond their original, as fabricated design remains as one of the challenging problems within the research field of architected materials. To that end, Kirigami - the art of cutting and folding flat sheets of paper, provides scalable routes to generate intricate three-dimensional shapes from thin, planar (two-dimensional) sheets of materials. Researchers have utilized mechanical force actuated Kirigami structures in functional disciplines as diverse as energy harvesting, actuation, optics, stretchable electronics, and soft robotics. Achieving shape reconfiguration of freestanding, Kirigami-cut sheets in a stimuli-responsive, autonomous manner would not only enable new functionalities but also contribute to self-assembly.

This work aims to understand the self-folding behavior of Kirigami-cut bilayers where one layer isotropically expands with respect to the other in response to an external stimulus. We investigate two distinct types of cut geometries namely squares with radial cuts and rectangles with side cuts through a combination of nonlinear finite element modeling and experiments with soft polymeric systems. The Kirigami cuts decompose the pristine squares and rectangles into interconnected beams (length >> width) and plates (length ~ width) of varying aspect ratios. Our finite element calculations reveal that it is possible to tune both the bending direction and curvature values of each individual geometric units within the Kirigami-cut structures and thus transform the bilayers into complex three-dimensional architectures with spatially varying bi-directional curvatures in an on-demand manner. To experimentally demonstrate the potential of our approach, we design planar bilayered samples with side cuts and swell them in organic solvents to generate letters from the English alphabet to make up "UIUC" (University of Illinois at Urbana–Champaign) and "MRS" (Materials Research Society). We also design bilayers with radial cuts, and as they transform shapes with varying mismatch strains (solvent concentrations), we show that it is possible to use them as freestanding tunable optical systems where the transmission and reflection windows for incident light could be controlled through the deformation behavior of individual geometric units between the cuts. We also use a combination of the cuts to realize polyhedral shapes (such as tetrahedron and cube) through the self-folding of planar bilayers. The design principles proposed in this work would be applicable to a variety of material systems across length scales and contribute toward the development of smart programmable metamaterials.