Wriggers P. Computational Contact Mechanics

2-nd edition. Springer, Berlin, 2006, 519 pp.
Contact mechanics has its application in many engineering problems. No one can walk without frictional contact, and no car would move for the same reason. Hence contact mechanics has, from an engineering point of view, a long history, beginning in ancient Egypt with the movement of large stone blocks, over first experimental contributions from leading scientists like Leonardo da Vinci and Coulomb, to today’s computational methods. In the past contact conditions were often modelled in engineering analysis by more simple boundary conditions since analytical solutions were not present for real world applications. In such cases, one investigated contact as a local problem using the stress and strain fields stemming from the analysis which was performed for the entire structure. With the rapidly increasing power of modern computers, more and more numerical simulations in engineering can include contact constraints directly, which make the problems nonlinear.
This book is an account of the modern theory of nonlinear continuum mechanics and its application to contact problems, as well as of modern simulation techniques for contact problems using the finite element method.Introduction to Contact Mechanics
Continuum Solid Mechanics and Weak Forms
Contact Kinematics.
Constitutive Equations for Contact Interfaces
Contact Boundary Value Problem and Weak Form
Discretization of the Continuum
Discretization, Small Deformation Contact
Discretization, Large Deformation Contact
Solution Algorithms
Thermo-mechanical Contact
Beam Contact
Computation of Critical Points with Contact Constraints
Adaptive Finite Element Methods for Contact Problems
Appendix