Computational Contact Mechanics

Contact mechanics is a specialist area in engineering mechanics. Itdeals with non standard mechanics which frequently appear in realtechnical applications. Examples include the simulation of carcrashes, human joints, car tyres, rubber seals and metal formingprocesses. Modern numerical simulation methods are used to modelthese objects and their behaviour.
Contact problems are an area of great technical importance inindustrial applications in mechanical and civil engineering,however only very few problems involving contact can be solvedanalytically. For most industrial applications, numerical methodshave to be applied since the contacting bodies have complexgeometries, undergo large deformations (including time dependentresponses) or are affected by other factors. The range ofapplications starts with relatively simple problems such asfoundations or bearings, and includes metal forming processes,rubber sealings, drilling problems, crash analysis of cars, andeven biomechanics, where human joints, implants or teeth are underconsideration. Although other numerical and analytical schemes canalso be used, this book concentrates mainly on finite elementtechniques for the treatment of contact problems, including newapproaches such as adaptive finite element methods.
* At the cutting edge of an area of significant (and growing)interest in computational mechanics
* Covers the theoretical background of simulations and discussesmodern numerical simulation methods
* Relates to many engineering applications
A valuable reference resource for graduate and postgraduatestudents, as well as engineers involved in numerical simulation inindustry (e.g. aeronautics, car and tyre design, biomechanics,metal forming). Preface.

Introduction.

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.

Adaptive Finite Element Methods for Contact Problems.

Computation of Critical Points with Contact Constraints.

Appendix A: Gauss Integration Rules.

Appendix B: Convective Coordinates.

Appendix C: Parameter Identification for Friction Materials.

References.

Index.

Peter Wriggers is the author of Computational Contact Mechanics, published by Wiley. Boundary value problems involving contact are important for industrial applications in both mechanical and civil engineering, such as structural foundations, bearings, metal forming processes, rubber sealings, drilling problems, crash analysis of cars, rolling contact between car tyres and the road, cooling of electronic devices, and many more. Other applications are related to biomechanical engineering design, where human joints, implants or teeth are considered. Due to this variety, contact problems today are combined either with large elastic or inelastic deformations, including time-dependent responses. Thermal coupling may also have to be considered, and even stability behaviour has to be linked to contact, such as wrinkling arising in metal forming problems.

The topic of computational contact is described in depth here, providing different formulations, algorithms and discretisation techniques for contact problems that have been established in the geometrically linear and nonlinear ranges. This book provides the necessary continuum mechanics background. Special geometrical relations needed to set up the contact constraints are derived, and constitutive equations stemming from tribology which are valid at the contact interface are discussed in detail, without going into a numerical treatment. Solid and beam contact is considered, as is contact of unstable systems and thermomechanical contact. The algorithmic aspects cover a broad range of solution methods. Additionally, adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations.

This book:

• applies to a wide variety of industrial applications,
• starts from a sound continuum mechanics background,
• introduces new discretisation techniques and algorithms, and
• includes thermo-mechanical considerations and adaptive methods.

Computational Contact Mechanics has been written not only for graduate, Masters and PhD students, but also for engineers in the car, tyre and packaging industries who simulate contact problems in practical applications and need to understand the theoretical and algorithmic background of contact treatment in modern finite element systems.