Conical differentiability for bone remodeling contact rod models

Abstract

We prove the conical di erentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary di erential equation with respect to time. This structure enables the veri cation of the two following fundamental results: the polyhedricity of a modi ed displacement constraint set de ned by the obstacle and the di erentiability of the two forms associated to the variational inequality.