1 Introduction
1．1 Goal of This Book
1．2 Method of Dimensionality Reduction as the Link Between the Micro- and Macro-Scales
1．3 Structure of the Book
References
2 Separation of the Elastic and Inertial Properties
in Three-Dimensional Systems
2．1 Introduction
2．2 The Quasi-Static State
2．3 Elastic Energy as a Local Property
2．4 Kinetic Energy as a Global Property
2．5 Problems
References
Normal Contact Problems with Axially-Symmetric Bodies
3 Without Adhesion
3．1 Mapping of Three-Dimensional Contact Problems onto One Dimension： The Basic Idea
3．2 The Rules of Geike and Popov and the Rules of HeB for Normal Contact Problems
3．3 General Mapping of Axially-Symmetric Profiles
3．4 The Mapping of Stress
3．5 The Mapping of Non-Axially-Symmetric Bodies
3．6 Problems
References
4 Normal Contact with Adhesion
4．1 Introduction
4．2 Rule of Hel3 for the Adhesive Contact Between Axially-Symmetric Bodies
4．3 The Adhesive Contact and Griffith Crack
4．4 Full Reduction of the Adhesive， Elastic Contact
4．5 Example： Adhesion of a Sphere with a Superimposed Radial Waveform
4．6 Problems
References
5 Tangential Contact
5．1 Introduction
5．2 Tangential Contact with Friction for Parabolic Bodies
5．3 Tangential Contact with Friction for Arbitrary Axially-Symmetric Bodies
5．4 Mapping of Stresses in the Tangential Contact
5．5 Mapping of Local Slip
5．6 Problems
References
6 Rolling Contact
6．1 The Mapping of Steady-State Rolling Contacts
6．2 Rules for the Exact Mapping of Rolling Contacts
6．3 Shakedown and Creep in Oscillating Rolling Contacts
6．4 Problems
References
7 Contacts with Elastomers
7．1 Introduction
7．2 Stress Relaxation in Elastomers
7．3 Application of the Method of Dimensionality Reduction in Viscoelastic Media： The Basic Idea
7．4 Radok's Method of the Functional Equations
7．5 Formulation of the Reduction Method for Linearly Viscous Elastomers
7．6 The General Viscoelastic Material Law
7．7 Problems
References
8 Heat Transfer and Heat Generation
9 Adhesion with Elastomers
10 Normal Contact of Rough Surfaces
11 Frictional Force
12 Frictional Damping
13 The Coupling to Macroscopic Dynamics
14 Acoustic Emission in Rolling Contacts
15 Coupling to the Microscale
16 And Now What?
17 Appendix 1： Exact Solutions in Three Dimensions for the Normal Contact of Axially-Symmetric Bodies
18 Appendix 2： Exact Solutions in Three Dimensions for the Tangential Contact of Axially-Symmetric Bodies
19 Appendix 3： Replacing the Material Properties with Radok's Method of Functional Equations
20 Appendix 4： Determining Two-Dimensional Power Spectrums from One-Dimensional Scans
Index
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