𝐻2-Conformal Approximation of Miura Surfaces

Abstract The Miura ori is a very classical origami pattern used in numerous applications in engineering. A study of the shapes that surfaces using this pattern can assume is still lacking. A constrained nonlinear partial differential equation (PDE) that models the possible shapes that a periodic Miura tessellation can take in the homogenization limit has been established recently and solved only in specific cases. In this paper, the existence and uniqueness of a solution to the unconstrained PDE is proved for general Dirichlet boundary conditions. Then an H 2 H^{2} -conforming discretization is introduced to approximate the solution of the PDE coupled to a Newton method to solve the associated discrete problem. A convergence proof for the method is given as well as a convergence rate. Finally, numerical experiments show the robustness of the method and that nontrivial shapes can be achieved using periodic Miura tessellations.