Preface ........................................................ xi
1 Introduction ................................................. 1
1.1 Historical notes ........................................ 1
2 Dry friction and damped oscillators .......................... 5
2.1 Amontons' law ........................................... 5
2.2 Applications to representative mechanical systems ....... 7
2.3 Viscous friction ....................................... 12
Part I Elastic Contacts ....................................... 17
3 Elements of the theory of elasticity ........................ 19
3.1 Strain ................................................. 19
3.2 Stress ................................................. 20
3.3 Isotropic elastic materials ............................ 21
3.4 Equilibrium of elastic bodies .......................... 24
3.5 Elastic waves .......................................... 25
4 Normal contacts ............................................. 27
4.1 Pressure on an elastic half-space ...................... 27
4.2 Indentation of an elastic half-space ................... 31
4.3 The Hertz theory ....................................... 33
4.4 Beyond the Hertz theory ................................ 39
4.5 Influence of friction on normal contact ................ 41
5 Tangential contacts ......................................... 44
5.1 Traction on an elastic half-space ...................... 44
5.2 Partial slip ........................................... 46
5.3 Sliding of elastic objects ............................. 50
5.4 Influence of oscillating forces ........................ 52
6 Elastic rolling ............................................. 54
6.1 Steady elastic rolling ................................. 54
6.2 Three-dimensional rolling .............................. 57
6.3 Sphere in a groove ..................................... 59
6.4 Tire mechanics ......................................... 60
7 Beams, plates and layered materials ......................... 62
7.1 Elastic deformation of beams ........................... 62
7.2 Plate theory ........................................... 66
7.3 Elastic instabilities .................................. 68
7.4 Shells ................................................. 69
7.5 Indentation of elastic plates .......................... 70
7.6 Indentation of thin elastic layers ..................... 71
Part II Advanced Contact Mechanics ............................ 73
8 Rough contacts .............................................. 75
8.1 Surface roughness ...................................... 75
8.2 Early models of rough contacts ......................... 78
8.3 The Persson theory ..................................... 81
8.4 Advanced concepts in the Persson theory ................ 85
8.5 Contact of wavy surfaces ............................... 88
9 Viscoelastic contacts ....................................... 90
9.1 Stress-strain relation ................................. 90
9.2 Constitutive models .................................... 92
9.3 Viscoelastic indentation ............................... 95
9.4 Rubber friction ........................................ 97
9.5 Rolling on viscoelastic bodies ......................... 99
10 Adhesive contacts .......................................... 101
10.1 The Johnson-Kendall-Roberts model ..................... 101
10.2 The Derjaguin-Muller-Toporov model .................... 102
10.3 The Maugis-Dugdale model .............................. 103
10.4 The Persson theory with adhesion ...................... 105
10.5 Adhesion in biological systems ........................ 108
11 Thermal and electric effects ............................ 109
11.1 Thermal effects in polymers ........................... 109
11.2 Flash temperature ..................................... 110
11.3 Heat transfer between rough surfaces .................. 112
11.4 Electric contact resistance ........................... 113
12 Plastic contacts ........................................... 115
12.1 Plasticity ............................................ 115
12.2 Criteria of yielding .................................. 118
12.3 Plastic flow .......................................... 120
12.4 Plastic indentation ................................... 120
12.5 Compression and traction of a plastic wedge ........... 122
12.6 Hardness .............................................. 124
12.7 Plowing ............................................... 125
12.8 Elastic-plastic indentation ........................... 126
12.9 Rolling on plastically deformed bodies ................ 129
12.10 Rough plastic contacts ............................... 130
12.11 Plasticity of geomaterials ........................... 131
13 Fracture ................................................... 133
13.1 Fracture modes ........................................ 133
13.2 The Griffith criterion ................................ 135
13.3 Dynamic fracture ...................................... 136
13.4 Fracture in rubber-like materials ..................... 138
14 Stick-slip ................................................. 140
14.1 Stick-slip ............................................ 140
14.2 Contact ageing ........................................ 141
14.3 Lubricated friction ................................... 142
14.4 The Burridge-Knopoff model ............................ 146
14.5 Plastic flow .......................................... 148
14.6 Earthquakes ........................................... 151
Part III Nanotribology ........................................ 153
15 Atomic-scale stick-slip .................................... 155
15.1 The Prandtl-Tomlinson model ........................... 155
15.2 Energy barrier ........................................ 159
15.3 Thermal effects ....................................... 161
15.4 Long jumps ............................................ 163
15.5 Dynamic superlubricity ................................ 165
15.6 Constant driving force ................................ 165
15.7 The Frenkel-Kontorova model ........................... 168
15.8 Electronic and phononic friction ...................... 170
16 Atomic-scale stick-slip in two dimensions .................. 174
16.1 The Prandtl-Tomlinson model in two dimensions ......... 174
16.2 Structural lubricity .................................. 178
16.3 Sliding of adsorbate layers ........................... 180
17 Instrumental and computational methods in nanotribology .... 183
17.1 Atomic force microscopy ............................... 183
17.2 Other scanning probe modes ............................ 186
17.3 Other experimental techniques in nanotribology ........ 188
17.4 Molecular dynamics and nanotribology: methods ......... 190
17.5 Molecular dynamics and nanotribology: results ......... 191
18 Experimental results in nanotribology ...................... 196
18.1 Friction measurements on the atomic scale ............. 196
18.2 Lateral and normal stiffness .......................... 199
18.3 Load dependence of nanoscale friction ................. 200
18.4 Velocity dependence of nanoscale friction ............. 201
18.5 Temperature dependence of nanoscale friction .......... 202
18.6 Effect of contact vibrations .......................... 203
18.7 Friction anisotropy ................................... 204
19 Nanomanipulation ........................................... 207
19.1 Contact mode manipulation ............................. 207
19.2 Dynamic mode manipulation ............................. 208
19.3 Nanoparticle trajectories during AFM manipulation ..... 209
19.4 Lifting up molecular chains ........................... 214
20 Wear on the nanoscale ...................................... 216
20.1 Wear on the nanoscale ................................. 216
20.2 Surface rippling ...................................... 220
21 Non-contact friction ....................................... 224
21.1 Experimental methods to measure non-contact friction .. 226
21.2 Internal friction of cantilevers ...................... 228
21.3 Origins of non-contact friction ....................... 231
21.4 Giant non-contact friction ............................ 237
21.5 Near-contact friction ................................. 237
Part IV Lubrication ........................................... 241
22 Drag in a viscous fluid .................................... 243
22.1 The Navier-Stokes equation ............................ 243
22.2 Flow of a viscous fluid ............................... 245
22.3 Motion in a viscous fluid ............................. 247
22.4 Boundary layers and skin friction ..................... 250
22.5 Drag crisis ........................................... 253
22.6 Streamlined bodies .................................... 253
23 Lubrication ................................................ 256
23.1 Нуdrodynamic lubrication .............................. 256
23.2 Elastohydrodynamic lubrication ........................ 262
23.3 Hydrostatic lubrication ............................... 262
23.4 Solid lubrication ..................................... 263
24 Viscous phenomena in confined or spreading liquids ......... 265
24.1 The Eyring model ...................................... 265
24.2 Capillary bridges ..................................... 267
24.3 Fluid flow between rough surfaces ..................... 270
24.4 Squeezed films ........................................ 272
24.5 Spreading of liquids .................................. 275
Appendix A Friction force microscopy ......................... 278
Appendix В Viscosity of gases ................................. 282
Appendix С Slip conditions .................................... 284
References .................................................... 285
Index ......................................................... 301
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