While the impact of mechanical loading of articular cartilage on the onset and progression of osteoarthritis is well known, the actual mechanisms of this connection remain unclear. One reason is that in-vivo measurements of the stress and strain distribution within the cartilage are currently impossible for common motions.

This project aims at estimating stress distributions in knee cartilate from gait data, by coupling a multibody model of the lower limb to a finite element model of the knee. The inverse problem leads to a large optimization problem with nonsmooth contact mechanics as equality constraint. For its solution, we investigate affine covariant composite step methods with an augmented Lagrangian relaxation of the contact constraints. For the latter, we develop a matching multigrid with overlapping QP smoothers.