These days, the choice of the optimal surgical procedure still relies heavily on the experience of the surgeon and even small misjudgements can cause detrimental long-term effects. Therefore preoperative planning is very important to reduce these unwanted effects. This project aims to develop a virtual lab that allows for the preoperative assessment or optimization of various surgical options and parameters. In particular, we are interested in the dynamic simulation of joint mechanics and the design of individually shaped implants. This requires the development of robust numerical techniques for the spatially and temporally resolved simulation of the biomechanics of heterogeneous tissues as well as efficient optimization algorithms. The variety of tissue materials leads to heterogeneous domain decomposition problems. Due to large deformations of soft tissue and contact between implant, bone, and soft tissue, these problems involve non-convex non-linear hyperelastic and bi-phasic contact problems.