Curvature Induced by Deflection in Thick Meta-Plates

Mohammad J. Mirzaali*, Aref Ghorbani, Kenichi Nakatani, Mahdiyeh Nouri-Goushki, Nazli Tümer, Sebastien J.P. Callens, Shahram Janbaz, Angelo Accardo, José Bico, Mehdi Habibi, Amir A. Zadpoor

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
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The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

Original languageEnglish
Article number2008082
Number of pages11
JournalAdvanced Materials
Issue number30
Publication statusPublished - 2021


  • 3D printing
  • auxeticity
  • functional materials
  • Gaussian curvature
  • mechanical metamaterials


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