Macroscopic deformation modes of origami tessellations and periodic pin-jointed trusses: the case of the eggbox

Hussein Nassar (1, 2) , Arthur Lebée (1) , Laurent Monasse (2)

1 navier umr 8205 - Laboratoire Navier
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms at a local scale aggregate and bring on large changes in shape, curvature and elongation at a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces. This paper characterizes the parametrization, curvature and metric of smooth surfaces that the eggbox pattern can fit asymptotically, i.e., when the eggbox unit cell parameter becomes infinitely small compared to the typical radius of curvature of the target surface. In particular, it is demonstrated that no finite region of a sphere can be fitted and a systematic method that allows to fit ruled surfaces is presented. As an application, the fitting of a one-sheeted hyperboloid is constructed.

Keywords: Origami; metasurface; form finding; floppy modes; eggbox

Domains: Solid mechanics [physics.class-ph]

Hussein Nassar, Arthur Lebée, Laurent Monasse. Macroscopic deformation modes of origami tessellations and periodic pin-jointed trusses: the case of the eggbox. IASS Annual Symposium 2017 “Interfaces: architecture, engineering, science”, Sep 2017, Hambourg, Germany. ⟨hal-01691183⟩