Computational Contact Mechanics
September 25, 2006 — September 29, 2006
- Tod A. Laursen (Duke University, Durham, N. Carolina, USA)
- Peter Wriggers (Leibniz Universität Hannover, Hannover, Germany)
Within the last years, computational contact mechanics has been a topic of intense research. The aim of the development is to devise robust solution schemes and new discretization techniques which can be applied to finite deformation contact problems when using higher order interpolations. The main focus of this course is to convey modern techniques applied within the range of computational contact mechanics.
The topics of interest are wide ranging, including computational aspects of (1) discretization techniques for problems with small and finite deformations (2) solution algorithms for single- and multi-processor computing environments (3) multi-scale approaches to contact problems (4) integration methods for rolling contact problems (5) discrete element models for contact and (6) multi-field problems with contact constraints.
The lectures will cover the background like a short introduction to continuum mechanics and finite element methods, but will in depth treat the theoretical formulation of contact problems with regard to mechanics and mathematics. Furthermore discretization schemes for two- and three-dimensional contact problems of small and large deformations will be discussed. These schemes include also formulations for rolling contact applications. Solution techniques related to contact mechanics are also of interest. Here lectures on solvers for large-scale multi-contact problems will be given. This includes multi-scale contact related to quasi-static, dynamical, structural and granular applications. Special attention is also given to conjugate gradient algorithms and extensions. A set of lectures will be devoted to domain decomposition methods for structural problems and application to cellular materials and for homogenization techniques in micro-macro approaches for frictional problems. A set of lectures will cover discrete element techniques for multi body contact
analysis and their applications to industrial problems.
All lectures will be of theoretical and applied nature, suitable for graduate students of applied mathematics, mechanics, engineering and physics with interest in computer simulation of contact problems.