A Decomposition Approach for the Numerical Solution of Fristional Contact Problems in Nonlinear Elasticity

Contact problems occur in almost all situations of our life and they are usually connected to the touching of elastic bodies. Examples are gear boxes, tires, moving machine parts or prostheses. Simulation tools, which provide reliable predictions for the behavior of elastic bodies in contact, are therefore of high importance for many applications in engineering, industry and life sciences. There is a at least two-dimensional gap between the need of efficient simulation tools for contact problems and the availability of reliable and efficient simulation methods and their implementations. The first dimension of this gap can be found to be the still relatively low number of inherently nonlinear and nonsmooth decomposition methods, which can deal with the effects at the interfaces between the contacting bodies as well as with the nonconvexity arising from nonlinear material laws. The second dimension of this gap is the fact that many modern and mathematically sound methods are not implemented in a way, which makes them usable for the simulation of demanding applications. Even worse, many new methodological developments are tested only for simple model problems, and the robustness of new methods with respect to varying geometries, material laws, boundary conditions is often not investigated. It is the aim of this project to narrow this gap in both dimensions by developing, implementing and providing new solution strategies for frictional contact problems in nonlinear elasticity. This project is concerned with the development of highly efficient and reliable smooth and nonsmooth decomposition based discretization and solution strategies, which are applicable to frictional contact problems in nonlinear elasticity. To this end, we will exploit the power of state of the art ideas from nonlinear domain decomposition, optimization and nonsmooth minimization for the development of new tools for numerical simulations in frictional contact mechanics; we will also put considerable emphasis on the implementation of these methods, in order to make them applicable to real world problems. By providing theoretically well designed and modern solution methods, which are moreover implemented in a flexible framework and tested along realistic problems, we will provide a sound basis for improving the quality of numerical simulation in many important application areas, ranging from engineering over medicine to life sciences.