Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II

Filipe A. dos Santos, Antonino Favata, Andrea Micheletti, Roberto Paroni, Marco Picchi Scardaoni

Research output: Contribution to journalArticlepeer-review


In Part I of this study, it was shown that all the three known types of monohedral hexagonal tessellations of the plane, those composed of equal irregular hexagons, have just a single deformation mode when tiles are considered as rigid bodies hinged to each other along the edges. A gallery of tessellated plates was simulated numerically to demonstrate the range of achievable deformed shapes. In Part II, the displacement field was first derived and a continuous interpolant for each type of tessellated plate. It turns out that all corresponding metasurfaces are described by quadrics. Afterwards, a parametric analysis was carried out to determine the effect of varying angles and edge lengths on the curvature, and the values of the geometric Poisson ratio of the plates. Finally, a method of fabrication is proposed based on the additive manufacturing of stiff tiles of negligible deformability and flexible connectors. Using this modular technique, it is possible to join together different monohedral tessellated plates able to deform into piece-wise quadrics. The nodal positions in the deformed configuration of the realized plates are measured after enforcing one principal curvature to assume a chosen value. The estimate of the other principal curvature confirms the analytical predictions. The presented tessellated plates permit to realize doubly curved shape-morphing metasurfaces with assorted shapes, which also can feature a certain surface roughness, and they can be employed in all applications demanding high surface accuracy and few actuators or just one.
Original languageEnglish
Article number20230449
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2284
Publication statusPublished - 28 Feb 2024


  • metasurface
  • morphing structure
  • rigid microstructure
  • tessellation
  • three-dimensional printing


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