Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet’s material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.
J. L. Silverberg, J.-H. Na, A. A. Evans, B. Liu, T. C. Hull, C. D. Santangelo, R. J. Lang, R. C. Hayward, I. Cohen, “Origami structures with a critical transition to bistability arising from hidden degrees of freedom”, Nat. Mater. DOI: 10.1038/nmat4232 (2015) pdf SI
Patterning deformation within the plane of thin elastic sheets represents a powerful tool for the definition of complex and stimuli-responsive 3D buckled shapes. Previous experimental methods, however, have focused on sheets that access a limited number of shapes pre-programmed into the sheet, restricting the degree of dynamic control. Here, we demonstrate on-demand reconfigurable buckling of poly(N-isopropylacrylamide-co-acrylic acid) (PNIPAM) hydrogel network films containing gold nanoparticles (AuNPs) by patterned photothermal deswelling. Predictable, easily controllable, and reversible transformations from a single flat gel sheet to numerous different three-dimensional forms are shown. Importantly, the response time is limited by poroelastic mass transport, rather than photochemical switching kinetics, enabling reconfiguration of shape on timescales of several seconds, with further increases in speed possible by reducing film thickness.
A. W. Hauser, A. A. Evans, J.-H. Na, R. C. Hayward, Angew. Chem. Int. Ed., DOI: 10.1002/anie.201412160 (2015) pdf SI
Developments in origami mathematics over the past few dec-ades have enabled the systematic design of folded structures with arbitrary complexity, extending the capabilities of the form well beyond the diversity of shapes achieved with traditional paper art, and highlighting its power as a tool for the fabrication of 3D objects from 2D sheets. More recently, an area of considerable interest has been the development of self- folding structures that undergo autonomous transformations between programmed shapes in response to external triggers or changes in their environment. The ability to use origami design principles to controllably fold, unfold, and refold thin sheets prepared by planar fabrication techniques would offer great promise for applications in biomimetic systems, soft robotics, and mechanical metamaterials, especially for fabrication of structures on small length scales, where traditional manufacturing processes fail.
J.-H. Na, A. A. Evans, J. Bae, M. C. Chiappelli, C. D. Santangelo, R. J. Lang, R. C. Hayward, Adv. Mater., 27 79-85 (2015) pdf SI
When a flexible filament is confined to a fluid interface, the balance between capillary attraction, bending resistance, and tension from an external source can lead to a self-buckling instability. We perform an analysis of this instability and provide analytical formulae that compare favorably with the results of detailed numerical computations. The stability and long-time dynamics of the filament are governed by a single dimensionless elastocapillary number quantifying the ratio between capillary to bending stresses. Complex, folded filament configurations such as loops, needles, and racquet shapes may be reached at longer times, and long filaments can undergo a cascade of self-folding events.
A. A. Evans, S. E. Spagnolie, D. Bartolo, and E. Lauga, Soft Matter, 9 1711-1720 (2013) pdf