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