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| Silhavy M. — The Mechanics and Thermodynamics of Continuous Media |
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| Предметный указатель |
Absolute temperature 76
Absolute temperature scale, ideal gas temperature 126
Absolute temperature scale, uniqueness 124
Accessibility axiom 90 98 100 128 134
Accumulation function 113 133
Acoustic tensor 411
Acoustic tensor of fluids 422
Acoustic tensor of isotropic solids 423
Acoustic tensor, isothermal 346
Acoustic tensor, referential 411
Acoustic tensor, spatial 411 421—423
Additivity of measures 110
Additivity of the set of cyclic heating measures 122
Adiabat, Hugoniot’s 446 447
Adiabat, odrinary 119
Adiabat, ordinary 120
Adiabatic dynamics, balance equations 406
Adiabatic dynamics, constitutive equations of 406
Adiabatic dynamics, first-order system 409
Adiabatic dynamics, isentropic dynamics 407
Adiabatic fluid dynamics, characteristic equation 444
Adiabatic fluid dynamics, equations of 443
Adiabatic isolation 211
Admissibility criterion, entropy criterion 434 452
Admissibility criterion, entropy rate criterion 439
Admissibility criterion, Lax’s criterion 437
Admissibility criterion, Liu’s criterion 438 452
Admissibility criterion, viscosity criterion 435 436
Admissibility criterion, viscosity profile 437
Admissible region 29
Anomalous behavior 291
Apparent force 102 106
Balance of angular momentum 74
Balance of energy 75 76 461
Balance of linear momentum 73
Balance, general balance equation 67—69
Body force 73
Body, continuous 29
Body, material 94
Body, part of 30 61
Body, state function of 94
Body, state space of 94
Body, viscous with heat conduction 151
Borel sets 110
Canonical free energy 211 314 340 382
Carnot process 119 122
Cauchy’s equations 107
Change of frame 101
Change of variables 168
Characteristic, amplitude 413
Characteristic, equation 347 412
Characteristic, field 414
Characteristic, pair 413
Characteristic, polynomial 11 347 416
Characteristic, space 412
Characteristic, speed 412 413
Characteristic, vector 412
chemical potential 194
Classical efficiency estimate 125 127
Classical spacetime 33
Clausius inequality 124
Clausius — Duhem inequality with the explicit production of entropy 461
Clausius — Duhem inequality, basic formulation 76 127
Clausius — Duhem inequality, control volume form 77
Clausius — Duhem inequality, derivation 128
Clausius — Duhem inequality, interpretations 78
Clausius — Duhem inequality, reduced form 76
Coercivity 344
Collection of bodies 96 121—124
Compatibility relations 190
Compliances 174
Configuration 34
Confinement condition 211
Conjugate function 263
Constitutive equation 91
Constitutive function 91 151
Contact forces 72
Contact heating 211
Convergence, strong, weak 370
Convex set 255
CYCLE 90
Cyclic work-heat pairs 96 132 133
Decrease of energy in isentropic shocks 408
Deformation, definition 34
Deformation, gradient 35
Deformation, homogeneous 39
Deformation, one-dimensional 40
Deformation, pairwise homogeneous 39
Deformation, periodic 40
Deformation, piecewise homogeneous 41
Density of mass 70
Discontinuity 426
Discontinuity contact 428 433 445
Discontinuity in fluids 445
Discontinuity, rest 428
Displacement 334 462
Dissipation 463
Dissipation inequality 77
Dissipation inequality internal 153
Dissipation potential 201
Dissipation principle 153
Dissipation principle for supply-free processes 162
Elasticities of fluids 195
Elasticities, adiabatic 179 189
Elasticities, at isotropic states 188—191
Elasticities, Cauchy’s tensor of 195
Elasticities, isothermal 188
Elasticities, referential tensor of 174
Energy 194
Energy criterion of stability 249
Energy identities 465 475
Energy, as independent variable 171
Energy, boundedness from below 104
Energy, internal 107
Energy, internal and kinetic 211
Energy, specific internal 75
Enthalpy 194 444
entropy 211
Entropy, as independent variable 170
Entropy, definition 127
Entropy, nonuniqueness 127 129
Entropy, specific 76
Entropy, total 76
Entropy, total production of 212
Equilibrium, state 210
Equilibrium, state, compatible with the conservative environment 231
Eshelby tensor 172
Eshelby tensor, referential 77 239 241
Eshelby tensor, total 220
Eshelby’s conservation law for bulk matter 232
Eshelby’s conservation law, dynamical 408
Eshelby’s conservation law, general 283
Eshelby’s conservation law, Noether’s theorem 241
Euler’s identities 37
Fatou’s Lemma 373
Fenchel transformation 263
First law 95
Fluid 158
Fluid of grade 2 200
Fluid, reversible 117
Flux of mass 71
Frechet differential 10
Free energy 77 194
Free part of the boundary 211
Function of bounded variation 110
Function, convex 257
Function, isotropic 137
Function, objective-isotropic 144
Function, response 151
Function, symmetric 139
| Garding’s inequality 351
Gibbs equations 154
Gibbs free energy 194
Gibbs function 194 323—326
Gibbs relation 329
Hadamard lemma 32 37 38
Hadamard material 193
Hadamard — Green material 192 423
Heat flux vector 75
Heat, absorbed, emitted 114
Heat, latent 180 181 195 282 402
Heat, net heat gained 95
Heat, specific 181
Heat, specific, at constant deformation 180
Heat, specific, at constant pressure 195
Heat, specific, at constant stress 181
Heat, specific, at constant volume 195
Heat, transformation law 104
Heating measure of a cyclic process 117
Heating measure, definition of 112
Heaviside function 110
Hugoniot, curves 433
Hugoniot, equations 426 448
Hugoniot, functions 448
Hugoniot, set 426
Hugoniot, set in fluids 446
Hull, convex 256
Hull, lower convex 260—262 391
Hull, lower polyconvex 391
Hull, lower quasiconvex 332 391
Hull, lowerrank 1 convex 391
Ideal gas 126
Imbedding theorem 339
Infinitesimal deformation tensor 183
Infinitesimal generator 468
Infinitesimal rotation tensor 183
Initial conditions 462
Inverse deformation 238
Inverse motion 172
Isometry 101
Isotherm 119
Isotropic solid 158
Jordan’s decomposition theorem 111
Joule’s relation 96
Jump 426
Jump in fluids 445
Jump, amplitude of 37
Kinetic, coefficients 197 403 463
Kinetic, equation for a phase boundary 402
Lax — Milgram lemma 473
Lax’s inequalities 437 452
Left stretch tensor 35
Legendre transformation, full 169
Legendre transformation, partial 168
Legendre — Hadamard condition 278 281 290 413
Liapunov function 244 465
Lie algebra 175
Linear momentum, transport 73
Linear semigroup 465
Linear semigroup, strongly continuous 468
Linearization 333—335 462 474
Local inversion theorem 365
Local state function 91
Local thermodynamic equilibrium 199
Lower semicontinuity 374 387
Lummer — Phillips theorem 469
Material time derivative 32
Material, adiabatic 152
Material, hyperbolic 413
Material, strictly hyperbolic 413
Material, thermoelastic 152
Material, uniformly dissipative 463
Material, viscous, with heat conduction 151
Maximum work 212
Maxwell’s construction 319
Maxwell’s relation 42 279—283 401—403
Mazur’s lemma 374
Measure, absolutely continuous 110
Measure, definition 110
Measure, Dirac’s 110
Measure, distribution function 110
Measure, Hausdorff 36 79
Measure, Lebesgue 79
Measure, positive, negative and total variations 111
Measure, probability 256
Measure, singular 110
Measure, support 111
Measure, Young measure 372
Measure, Young measure minimizer 393
Minors relations 380
Moving surface 30
Nonuniqueness in adiabatic dynamics 407 441
Null divergence 226
Null Lagrangian, at the boundary 273
Null Lagrangian, general 224—226
Null Lagrangian, homogeneous 221—224
Onsager’s relations 199
Partial inverse 168
Partial time derivative 36
Permutation symbol 13
Phase, simplex 261 323
Phase, splitting 261 323
Phase, splitting, unique 261 323
Piecewise continuous field 31 58
Piecewise continuously differentiable field 32 58
Piola’s transformation, identity 63
Poincare inequality 339
Point of convexity 256
Point of density, rarefaction 79
Point of strict convexity 257
Point of very strict convexity 259
Point, material 29
Polyconvexity 286 307 381
potential energy 214
Potential energy, volume and surface densities of 215
Principal stretches 35
Principle of material frame indifference 155
Principle of material frame indifference, active interpretation 102
Principle of material frame indifference, basic formulation 102
Principle of material frame indifference, fundamental aspect 101
Principle of material frame indifference, practical aspect 155
Principle of material frame indifference, transformation laws 102
Principle of maximum entropy 244 249 316
Principle of minimum canonical free energy 244 249
Principle of minimum energy 249 269 279 316
Process, adiabatic 113 120
Process, admissible 151
Process, centered 424
Process, continuation of 90 120
Process, cyclic process 90
Process, isothermal 113
Process, segment of 90
Process, transform under a change of frame 102
Quasiconvexity 268 387 391
Quasiconvexity at the boundary 272 346 357
Quasiconvexity,  -quasiconvexity 268
Rank 1 connection 38 47
Rank 1 convexity 275 293
Rankine — Hugoniot conditions 445
Rate-independence 118
Reference configuration 29 94
Reference configuration, change of 157
Reference configuration, change of, for Young measures 394
Referential density of an extensive quantity 65
Referential flux vector 62
Referential gradient 32
Referential normal 30
Referential speed 30
Relaxation in materials 202
Relaxation of integral functionals 392
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