This book presents the mathematics behind the formulation, approximation, and numerical analysis of contact and friction problems. It also provides a survey of recent developments in the numerical approximation of such problems as well as several remaining unsolved issues. Particular focus is placed on the Signorini problem and on frictionless unilateral contact in small strain. The final chapters cover more complex, applications-oriented problems, such as frictional contact, multi-body contact, and large strain.
Finite Element Approximation of Contact and Friction in Elasticity will be a valuable resource for researchers in the area. It may also be of interest to those studying scientific computing and computational mechanics.
Part. I. Basic concepts
Chapter. 1. Introduction
Chapter. 2. Sobolev spaces
Chapter. 3. Signorini’s problem
Chapter. 4. Lagrange finite elements and interpolation
Part. II. Numerical approximation for Signorini
Chapter. 5. Finite elements for Signorini
Chapter. 6. Nitsche’s method
Chapter. 7. Mixed methods
Part. III. Extension to frictional contact and large strain
Chapter. 8. Tresca friction
Chapter. 9. Coulomb friction
Chapter. 10. Contact between two elastic bodies
Chapter. 11. Contact and self-contact in large strain
Franz Chouly is professor at the University of Burgundy (Dijon, France). His research is focused on the numerical analysis of partial differential equations and variational inequalities, finite element methods, and applications in fluid and solid mechanics.
Patrick Hild is professor at Paul Sabatier University (Toulouse, France). His research is focused on the numerical analysis of partial differential equations and variational inequalities, finite element methods, and applications in solid mechanics.
Yves Renard is professor at the National Institute of Applied Sciences of Lyon (INSA Lyon, France). His research interests include numerical methods in solid mechanics, approximation of contact and friction conditions, numerical analysis of partial differential equations, finite element based numerical modeling.