Contact problems : the legacy of L. A. Galin

L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English.

In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten.

In addition there are three essays by students of Galin, bringing the analysis up to date.

I.G. GoryachevaFeodor M. BorodichOlesya I. Zhupanska

Editor's Preface	p. ix
Biographical Sketch of L.A. Galin	p. xi
Chapter 1 A Review of Research before 1953	p. 1
1.1 Introduction	p. 1
1.2 Frictionless Plane Problems	p. 1
1.3 Plane Adhesive Contact Problems	p. 3
1.4 Plane Frictional Contact Problems	p. 4
1.5 Plane Contact between Two Elastic Bodies	p. 5
1.6 Three-Dimensional Contact Problems	p. 7
Chapter 2 Plane Elasticity Theory	p. 11
2.1 The Fundamental Equations	p. 11
2.2 Stresses and Displacements in a Semi-Infinite Elastic Plane	p. 21
Chapter 3 Plane Static Isotropic Contact Problems	p. 33
3.1 Boundary Conditions for Plane Contact Problems	p. 33
3.2 The Riemann-Hilbert Problem for the Half-Plane	p. 35
3.3 Frictionless Punch Problems - Introduction	p. 39
3.4 Frictionless Punch Problems - Theory	p. 41
3.5 Examples of Frictionless Problems	p. 44
3.6 Frictional Punch Problems - Theory	p. 49
3.7 Frictional Punch Problems - Examples	p. 51
3.8 Sliding Contact with Coulomb Friction	p. 55
3.9 A Two-Punch Problem	p. 58
Chapter 4 Moving Punches, and Anisotropic Media	p. 61
4.1 Introduction	p. 61
4.2 Dynamic Plane Isotropic Elasticity Theory	p. 62
4.3 Displacement - Stress Relations	p. 64
4.4 Boundary Value Problems for a Moving Punch	p. 66
4.5 Complex Variable Formulation for a Plane Anisotropic Elastic Body	p. 67
4.6 Contact Problems for an Anisotropic Half-Plane	p. 70
4.7 Stick-Slip Contact	p. 74
4.8 Contact of Two Elastic Bodies	p. 87
Chapter 5 Contact Problems in Three Dimensions	p. 91
5.1 The Papkovich-Neuber Solution	p. 91
5.2 Solutions of Laplace's Equation in Certain Curvilinear Coordinates	p. 95
5.3 Circular Punches	p. 98
5.4 The Green's Function for the Exterior of a Circular Disc	p. 101
5.5 Axisymmetric Frictionless Contact Problems	p. 105
5.6 Axisymmetric Contact with Prescribed Contact Region	p. 112
5.7 Loading Outside a Circular Punch	p. 112
5.8 Axi-Symmetric Contact Problems with Friction	p. 115
5.9 A Punch of Elliptic Cross-Section	p. 120
5.10 Forces and Moments on an Elliptical Punch	p. 131
5.11 A Punch of Arbitrary Cross-Section	p. 133
5.12 The Pressure of a Wedge-Shaped Punch with Plane Base	p. 136
5.13 A Slender Beam on an Elastic Body	p. 136
5.14 Contact of Two Elastic Bodies	p. 144
5.15 Contact between a Rigid Punch and a Clamped Plate	p. 145
Chapter 6 Viscoelasticity, Wear and Roughness	p. 153
6.1 Introduction	p. 153
6.2 The Laplace Transform	p. 153
6.3 2-D Orthotropic Viscoelastic Bodies	p. 155
6.4 Adhesive Contact for a Viscoelastic Half-Plane	p. 157
6.5 Viscoelastic Rolling Contact	p. 165
6.6 The Limiting Case of Rolling of a Cylinder on a Viscoelastic Base	p. 177
6.7 Contact Problems in the Presence of Wear	p. 183
6.8 Axisymmetric Contact Problems in the Presence of Wear	p. 186
6.9 Plane Contact Problems for Rough Elastic Bodies	p. 190
6.10 Contact Problems for Rough Axisymmetric Elastic Bodies	p. 195
References	p. 199
Index	p. 205
Development of Galin's Research in Contact Mechanics	p. 207
1 Two-Dimensional Sliding Contact of Elastic Bodies	p. 207
1.1 Problem Formulation	p. 207
1.2 Contact Problem for a Cylinder	p. 210
1.3 Contact Problem for a Flat Punch	p. 212
2 Contact Problem with Partial Slip for the Inclined Punch with Rounded Edges	p. 217
2.1 Problem Formulation	p. 218
2.2 Contact Pressure Analysis	p. 220
2.3 Shear Stress Analysis	p. 225
2.4 Tensile Stress Analysis	p. 230
2.5 Results and Discussions	p. 232
2.6 Conclusions	p. 236
2.7 Appendix	p. 237
3 Three-Dimensional Sliding Contact of Elastic Bodies	p. 238
3.1 The Friction Law Has the Form [sigma subscript xz] = [rho]p	p. 239
3.2 The Friction Law Has the Form [sigma subscript xz] = [tau subscript 0] + [rho]p	p. 242
4 Periodic Contact Problem	p. 244
4.1 One-Level Model	p. 245
4.2 Principle of Localization	p. 248
4.3 System of Indenters of Various Heights	p. 250
4.4 Stress Field Analysis	p. 252
Hertz Type Contact Problems for Power-Law Shaped Bodies	p. 261
1 Introduction	p. 261
1.1 Hertz Type Contact Problems for rigid Indenters	p. 261
1.2 Formulation of a Hertz Type Contact Problem	p. 262
2 Frictionless Axisymmetric Contact	p. 264
2.1 The Galin Solution for Frictionless Axisymmetric Contact	p. 264
2.2 The Sneddon Representation of the Galin solution	p. 264
2.3 The Galin Solution for Monomial Punches	p. 266
2.4 A Solution for Polynomial Punches	p. 267
3 Axisymmetric Contact Problems with Molecular Adhesion	p. 267
4 Adhesive (No-Slip) Axisymmetric Contact Problems	p. 270
4.1 Two-Dimensional Problem for a Punch with Horizontal Base	p. 270
4.2 Axisymmetric Adhesive Contact Problems for Curved Punches	p. 271
4.3 The Mossakovskii Solution for Adhesive Contact	p. 271
4.4 Solution to the Problem for Punches of Monomial Shape	p. 273
5 Self-Similar Contact Problems	p. 275
5.1 Similarity Transformations for Hertz Type Contact Problems	p. 277
5.2 Punches Described by Homogeneous Functions	p. 279
5.3 Punches Described by Parametric-Homogeneous Functions	p. 280
6 Hardness Measurements and Depth-Sensing Techniques	p. 283
6.1 Brief History of Hardness Measurements	p. 283
6.2 Depth-Sensing Techniques	p. 285
6.3 Adhesive (No-Slip) Indentation	p. 287
6.4 Similarity Considerations of 3D Indentation	p. 293
Further Developments of Galin's Stick-Slip Problem	p. 293
1 Introduction	p. 293
2 The Stick-Slip Problem in Galin's Formulation	p. 294
2.1 Refinements of Galin's Solution	p. 294
2.2 Solution of the Galin Stick-Slip Problem Due to Antipov and Arutyunyan	p. 298
2.3 Solution to the Galin Stick-Slip Problem Due to Spence	p. 303
3 Extensions to the Stick-Slip Contact Problem	p. 306
3.1 Arbitrary Load	p. 306
3.2 A Periodic System of Punches	p. 307
3.3 Self-Similarity Approach in Stick-Slip Contact Problems	p. 307

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