Computation of origami-inspired structures and mechanical metamaterials

Origami folds have found a large range of applications in Engineering as solar panels for satellites or to produce inexpensive mechanical metamaterials. This talk will first focus on the direct problem of computing the deformation of periodic origami surfaces. A homogenization process for origami folds proposed in [Nassar et al, 2017] and then extended in [Xu, Tobasco and Plucinsky, 2023], is first discussed.Computation of origami-inspired structures and mechanical metamaterials

The talk will then focus on the PDEs describing the Miura fold, which is a classical origami fold. We study existence and uniqueness of solutions and then propose a finite element method to approximate them.

In a second time, we will focus on the inverse problem of computing an optimal fold set approximating a given target surface. The folding of a thin elastic sheet is modeled as a two-dimensional nonlinear Kirchhoff plate with an isometry constraint.

We formulate the problem in the framework of special functions of bounded variation SBV, and propose to use a phase-field damage model and a Local Discontinuous  Galerkin method to approximate the solutions of this problem.

We prove that the approximation Γ-converges to the sharp interface model. Finally, some numerical examples are presented.