Thursday, 10 December 2020Speaker: Prof. Arthur LebéeEcole des Ponts ParisTech Continuum elasticity of Miura Tessellations |
Abstract
Origami tessellations are curved two-dimensional discrete shells folded out of a periodic crease pattern. Unlike solid shells, Origami tessellations can morph and access a space of configurations each characterized by the list of folding angles of all creases. Due to inextensibility constraints imposed by Origami kinematics, not all combinations of folding angles are admissible and so the space of admissible configurations, is a priori unknown. In this talk, we present a model of Origami tessellations as continuum, rather than discrete, elastic shells. Most importantly, we suggest an asymptotic theory that translates the local constraints imposed on folding angles into global constraints weighing on the effective elongations and curvatures of the tessellation. Thus, the theory provides a characterization of the space of kinematically admissible configurations as the set of solutions to a system of nonlinear PDEs. Furthermore, the elastic strain energy required by each configuration is calculated. In conclusion, the elastostatic equilibrium of the tessellation is formulated as a constrained continuous energy minimization problem. The theory is exemplified in the case of the Miura tessellation. Various finite deformation modes are successfully predicted and constructed numerically under suitable boundary conditions. Notwithstanding the costs of higher analytical complexity and lower accuracy, the suggested theory offers a deeper physical insight into the configuration space of Origami tessellations while significantly reducing calculation time. This compromise should therefore prove beneficial in time-sensitive applications, as for instance is the case when real-time control of Origami tessellations is desired.
Biography
Arthur Lebée is researcher at Laboratoire Navier since 2011 and is HDR since 2019. His interests are in multiscale modelling in mechanics which he applies from architectured materials to mechanics of structures. He is currently principal investigator of the ANR project ArchiMatHOS entitled: "Architectured materials designed with higher-order homogenization and topology optimization". He is also involved in timber structures design. His research is focused on the rolling-shear behavior of cross laminated plates used in high-rise wood buildings. Arthur Lebée is co-director of the CNRS International Research Project Coss&Vita between Fédération Francilienne de Mécanique and M&Mocs on "Mechanics of generalized continua and their applications to engineering materials and structures"