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Silhavy M. — The Mechanics and Thermodynamics of Continuous Media
Silhavy M. — The Mechanics and Thermodynamics of Continuous Media

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Название: The Mechanics and Thermodynamics of Continuous Media

Автор: Silhavy M.

Аннотация:

This book presents the non-linear theories of continuum thermomechanics. The author emphasizes issues that are foundational in nature and seeks results common to materials of arbitrary symmetry. The central part deals with thermoelastic bodies with heat conduction and viscosity, including the inviscid or ideal dissipationless bodies. A surprising variety of phenomena can be modeled within this framework. The main ideas can be transferred into more complicated theories of materials with memory or microstructure. A large portion is an extension of Gibbs' ideas to bodies of general symmetry by the methods of the calculus of variations. The interplay between the convexity properties of the stored energy functions, the resulting equations, and the physics is also discussed.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 524

Добавлена в каталог: 15.11.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $W^{l,p}$-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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