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 journalArticleAcademicpeer-review

2 Citations (Scopus)


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
JournalAdvanced Materials
Issue number30
Early online date13 Jun 2021
Publication statusPublished - 2021


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


Dive into the research topics of 'Curvature Induced by Deflection in Thick Meta-Plates'. Together they form a unique fingerprint.

Cite this