Approximation of an Elastic Rod with Self-Contact

The variational formulation of an elastic rod with an impenetrable surface surrounding the centerline corresponds to a nonsmooth optimization of cost functional $$\mathcal {J}$$ J with nonconvex inequality constraints and so presents many analytical and computational challenges in approximating the minima. We construct a sequence of approximate variational cost functionals $$\mathcal {J}_k$$ J k , corresponding to elastic rods with infinite energy barriers that enforce impenetrability constraints. Using this construction, we show strong convergence of minimizing configurations of $$\mathcal {J}_k$$ J k to the minimizer of $$\mathcal {J}$$ J and weak* convergence in $$[C(0,1)]^*$$ [ C ( 0 , 1 ) ] ∗ of contact forces induced by the repulsive potential to the contact forces of the minimizing configurations of $$\mathcal {J}$$ J .