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Truesdell C., Noll W. — The Non-Linear Field Theories Of Mechanics |
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Предметный указатель |
Infinitesimal visco-elasticity 116
Inflation of a tube 189 195 211 343 353
Internal constraints 69 73
Internal energy 294
Invariants of a tensor 22 seq.
Invariants, lists 30 seq.
Invariants, multilinear 30
Invariants, polynomial 28 30
Invariants, representation 27 32
Irreversible thermodynamics 373
Irrotational homogeneous history 67
Irrotational motion 67 75
Isentropic elasticity 33
Isochoric (see also Incompressible)
Isochoric homogeneous motions 74
Isochoric motion 39 55
Isothermal cyclic processes 372
Isothermal elasticity 133
Isothermal stability 330
Isotropic elastic material 139
Isotropic elastic material, response coefficients 140 seq.
Isotropic hyperelastic material 313 seq. 31 7
Isotropic incompressible elastic material 14 seq.
Isotropic material of differential type 94
Isotropic material, wave propagation 278 291
Isotropic materials 78 seq.
Isotropic tensor function 22 24 34
Isotropic tensor function, representation 32 34
Isotropy group of an elastic material 122
Isotropy group of hyperelastic subfluids 314 to 316
Isotropy group, Isotropiegruppe 76 79
Isotropy groups of hyperelastic materials 310 313
Isotropy, definition, Isotropie 358
John’s special theory of elasticity 349
Jump continuation 374
Kelvin effects 176 236 345
Kinetic stability 259
Kirchhoff’s special theory of elasticity 348
Korpern 337 342
Korteweg’s theory of capillarity 513 515
Lame coefficients of elasticity 116 11 7
Lame coefficients of viscosity 113
Lineal flow of second-grade fluids 510 513
Lineal flow, geradlinige Strdmung 429 432 441 445
Lineal oscillation flow 444 seq.
Linear tensor function 22 33
Linearly viscous material 114
Liquid crystals (subfluids, anisotropic fluids) 86 88 151 314 316 473 475 523 537
Local action, principle, lokale Wirkung 12 36 56
Local configuration 52
Local deformation 52
Localization of a motion 51 seq.
Locally viscometric motion 432
Longitudinal wave 268 280
Macromedium 391
Macroquantities in polar elastic materials 3
Magnitude of a tensor 15
mass density 38
Mass distribution 38
Material co-ordinates and description 37 39
Material connection 89
Material frame-indifference (principle) 36 44 296
Material functionals 431
Material isomorphism 59
Material of grade n 63
Material time derivative 39
Material uniformity of a body 59 90
Materially uniform elastic body 126
Materials of differential type 93 95 111
Materials of integral type 98 101
Materials of mixed integral-differential type 101
Materials of rate type 95 98
Maximum entropy, theorem on 380
Maxwellian fluid, Truesdell’s theory 515 520
Memory (see Fading memory)
Micromedium 391
Microquantities in polar elastic materials 3
Minimum free energy, theorem on 370
Minimum internal energy, theorem on 380
Mixture of interdiffusing materials 537 541
Moduli, apparent, Moduln 239 seq.
Molecular and continuum theories compared 5
Moment condition 258
Moment of momentum 40
Moments of a tensor 23
Moments of a tensor, their gradients 27
Momentum, Impuls 40
Monotone transformation, monotone Transformation 161
Mooney-Rivlin theory of rubber 349 to 354
Motion of a body, general description 38
Multilinear invariants 30
Multilinear tensor function 22 34
Multipolar elasticity 40 seq.
Murnaghan's coefficients of second-order elasticity 230
Natural state 306 311 322
Natural units of elasticity, time-lapse etc. 64
Navier-Stokes equations 476
Navier-Stokes theory of viscometry 113 seq. 467
Neo-Hookean theory of elasticity 350
Noll’s theorem on flows with constant stretch history 438
Noll’s theorem on simple fluids 81
Noll’s theorem on simple materials 66
Non-conductor of heat 384
Normal end effects 452 458
Normal stress in cone-and-plate flow 463
Normal stresses in simple shear 175 to 178
Normal-stress difference in Couette flow 449
Normal-stress function 436
Normal-stress function, modified 446
Normal-stress in a second-order fluid 493
Normal-stress in flow between coaxial cylinders 448
Normal-stress in flow between sliding cylinders 451
Notations, Bezeichnungen 13 16
O-F inequalities (ordered forces) 157
Objective quantity (see Frame-indifferent quantity)
Objectivity (see Frame-indifference)
One-dimensional problems 10
Order of a fluid, einer Fliissigkeit 491
Order of a material of integral type 99
Order of a simple material 109
Order of elasticity 228
Oriented media 389
Orthogonal tensor 15
Oscillations of second-grade fluids 50 seq.
P-C inequality (pressure-compression) 155
Partial gradient of a function of tensors 25
Particles, definition 3 7
Perfect elasticity 304
Perfect fluid 149
Perfect materials 296 298
Physical components 15
Piezo-caloric effect 356
Piola-Kirchhoff stress tensors 120 124 144 169 300 320
Pipes, flow inside 448 452
Plane infinitesimal waves 273 278
Plane problems in elasticity 204 208
Plane problems in second-order elasticity 246
Plasticity, Plastizitdt 8 420
Poiseuille flow 451 seq.
Poiseuille flow of Ericksen's anisotropic fluids 536
Polar decomposition theorem 52
Polar elastic materials 389 401
Polarization, electrical 385
Polynomial invariants 28 30
Potential, thermomechanical 299
Power series of tensors 21
Poynting effect 177 235 345
Poynting's experiments on torsion 23 7
Poynting's problem 193 352
Pressure, Druck 149
| Pressure, effect on wave speed 284 seq.
Principal forces 144 317
Principal invariants of a tensor 23 25
Principal stresses 143
Principal stretchings 472
Principal waves 279
Principal waves, compatibility conditions 286 288
Principal waves, fundamental theorems 280 seq.
Principle of determinism for constrained materials 70
Principle of determinism for stress, fur Spannungen 56
Principle of equipresence 359 seq. 364
Principle of fading memory 36 101 103
Principle of loca action, der lokalen Wirkung 12 36 56
Principle of material frame-indifference 44 296
Principle of material, its history 45 47
Principles of mechanical behavior 36
Process, dynamical 41
Product of tensors 15
Production of entropy 295
Propagation condition 268
Propagation speed 268
Propagation speed, second-order effects 288 291
Quadric of polarization 268
Quasi-equilibrated motions of incompressible bodies 208 214
Radial oscillations of cylinders and spheres 214 219 354
Reciprocal theorem of Adkins 207
Reciprocal theorem of Betti 324 seq.
Recollection of a history 102
Reduced constitutive equations 66 69 113 120
Reference configuration 48
Reiner, basic contributions of 9
Reiner-Rivlin fluids 477 480 486
Reissner's variational principle 328
Relative Cauchy-Green tensor 53
Relative deformation function 49
Relative deformation gradient 49
Relative rotation tensor 53
Relative stretch tensor 53
Representation of a vector-valued function 35
Representation of the gradient of an invariant 34
Representation theorem for isotropic tensor functions 32
Representation theorem for linear isotropic tensor functions 33
Representation theorem for tensor invariants 28
Representation theorem, basic, of Cauchy 29
Response function of an elastic material 119
Response function, Auswirkungsfunktion 296
Response function, hypo-elastic 404
Response functional 36 58 61
Retardation formulae of Coleman and Noll 110 111
Retardation of a history 109
Rheogoniometer of Weissenberg 464
Rheology, Rheologie 8
Rigidity, Starrheit 72
Rivlin and Topakoglu's interpretation of Signorini’s expansion 227 229
Rivlin's formula for the torsional modulus under extension 192 seq.
Rivlin, basic contributions of 9
Rivlin-Ericksen fluids 481 seq.
Rivlin-Ericksen tensors 54
Rivlin-Ericksen tensors, generalization 516
Rivlin’s solutions in elasticity 171 197
Rotating cylinders, flow between them 44 seq.
Rotation tensor, Drehungstensor 52
Rubber, experimental results 171 181
Rubber, theory of Mooney and Rivlin 349 354
S-E condition (strong ellipticity) 129 132 147
Second-grade fluids 504 513
Second-grade hyperelastic materials 397 to 400
Second-order effects in elasticity 229 246
Second-order effects in isotropic hyperelastic materials 344 346
Second-order elasticities, determination by wave speeds 290 seq.
Second-order fluids 100
Second-order wave speed 288 291
Secondary flow in tubes, in Rohren 497 504
Secondary flow, sekunddre Strdmung 463 seq.
Shear modulus, generalized 174 182
Shear-stress function 436
Shearing function 436
Shearing of hypo-elastic material 418 426
Shearing, rectilinear 76
Shearing, Schergeschwindigkeit 436
Shifter 49
Shock wave 3
Shock wave, welle 267
Signorini's expansion 219 227
Signorini’s special theory of elasticity 348
Simple extension 173 180
Simple fluids 13 78 79 81 427 513
Simple material 36 60 63 78
Simple material of order 109
Simple material, thermal equilibrium 298 301
Simple materials, basic properties 66 69
Simple shear of elastic bodies 174
Simple shearing 442 seq.
Simple shearing of second-grade fluids 506
Simple solids 78 81
Simultaneous invariant of several tensors 22 24 25 31
Small elastic deformations superimposed on large ones 116 117
Solutions in finite elasticity, approximate 219 267 347
Space-time 41
Spatial co-ordinates and description 37 39
Spatial gradient 39
Spatial time derivative 39
Special theories of elasticity 347 354
Speed of wave propagation 268
Speed of wave propagation, second-order effects 288 291
Spencer-Rivlin theorem on tensor invariants 31
Spheres, radial oscillations 217 219
Spherical co-ordinates 20
Spherical shell, inflation and eversion 195 344
Spin tensor 54
St. Venant’s special theory of elasticity 348
Stability 153
Stability of hyperelastic bodies 328 332
Stability theorem of Hadamard 253
Stability, elastic 252 260
Stability, kinetic 259
State 329
Static continuation 106 369 371
Static stability 328
Statics of Ericksen’s anisotropic fluids 528 530
Stokes* principle of viscosity 475 seq.
Stokesian fluid, Truesdell’s theory 485 488
Stoppelli’s theorem 138
Stored energy 302 312
Stored-energy function 302 312 315
Stored-energy function, convex 322
Straightening of a cylindrical sector 188 seq. 343
Strain impulse, Verformungssto 107 108
Strain-energy function 302 307 316 397
Strain-energy function, no experimental test of existence 344
Stress principle 40
Stress relation 297 300 313 368
Stress relation, inversion 327
Stress relaxation 47 10 369
Stress tensor, convected 67
Stress tensor, non symmetrical 389
Stress vector 40
Stress, principal axes 142
Stress, Spannung 39 seq.
Stress-entropy relation 367 seq.
Stress-entropy tensor 365
Stress-relaxation function 115
Stress-relaxation function, Coleman’s theorem 378
Stress-strain relation 119
Stretch history, constant 438 440
Stretch tensors, right and left 53
Stretching tensor 54
Structural and continuum theories compared 5
Subfluids (liquid crystals) 86 88 151—
Subfluids, flow problems 473 to 475
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