Simulating Self-Avoiding Isometric Plate Bending

Abstract: Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider a nonlinear two-dimensional Kirchhoff plate model which is augmented via addition of a tangent-point energy. The resulting continuous model energy is finite if and only if the corresponding deformation is injective, i.e. neither includes self-intersections nor self-contact. We propose a finite element method method based on discrete Kirchhoff triangles for the spatial discretization and employ a semi-implicit gradient descent scheme for the minimization of the discretized energy functional. Practical properties of the proposed method are illustrated with numerous numerical simulations, exploring the model behavior in different settings and demonstrating that our method is capable of preventing non-injective deformations.