Modeling and numerical treatment of elastic rods with frictionless self-contact

In this paper we present a hyperelastic rod model that takes into account self-contact forces. The model is based on Cosserat rod theory that incorporates shear, elongation, flexure and twist deformations. The problem of avoiding self-penetration of parts of the rod is handled by the introduction of a contact distance function and the incorporation of associated contact forces. We present a penalty method for the treatment of the multi-valued and non-differentiable contact law. We also describe an augmented Lagrangian formulation of this problem. We then give the details of the finite-element discretization of the elastic rod self-contact problem as well as some numerical examples.