Geometry and Mechanics of fibers: Some numerical models (Invited Talk)

Joint work with Romain Casati, Alexandre Derouet-Jourdan, and Gilles Daviet, publication of the proceedings of MEIS 2015; International audience; In this talk I will give an overview of our work on the simulation of fibers and entangled materials, such as hair, with a specific interest for virtual prototyping and computer graphics applications. I will first introduce a family of high-order, reduced models for discretizing Kirchhoff's equations for thin elastic rods in a both faithful and robust way. Such models are particularly well-suited for simulating in-extensible fibers subject to bending and twisting, and featuring an arbitrary curly resting geometry. Then I will show how such models can be coupled to frictional contact using the nonsmooth contact dynamics framework, and I will present a hybrid iterative solver suitable for robustly handling thousands packed fibers at reasonable frame rates. Finally, I will give some insights into the inverse modeling of fibers, consisting in taking an arbitrary curve geometry as input and inferring corresponding geometric and physical parameters of the simulator such that the input geometry corresponds to a stable configuration at equilibrium.