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Eringen A.C. (ed.) — Continuum physics (vol. 4) Polar and Nonlocal Field Theories
Eringen A.C. (ed.) — Continuum physics (vol. 4) Polar and Nonlocal Field Theories

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Название: Continuum physics (vol. 4) Polar and Nonlocal Field Theories

Автор: Eringen A.C. (ed.)

Аннотация:

The fourth volume of Continuum Physics is devoted to the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. The purpose here is a thorough and precise presentation of exact continuum theories on materially nonuniform or nonsimple bodies (bodies composed of single, dipolar, and deformable elements) that can respond to short- and long-range interparticle loads and fields. Most of these theories have acquired their present definitive forms during the last decade or so, even though basic ideas and certain limited or approximate developments on some of these theories can be traced back to the turn of the entury. With the explosive developments that have taken place during the last decade, continuum physics is now very rich, and the impossible dream of bridging the gap between classical phenomenological physics and atomic and molecular physics is in sight.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 274

Добавлена в каталог: 17.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute temperature      214
Additivity of set functions and nonlocality      85
Attenuating neighborhood      226
Attenuating neighborhood hypothesis      216
Axiom of causality      17
Axiom of equipresence      217
Axiom of impenetrability      210
Axiom of locality      209 210
Axiom of objectivity      30 251
Balance laws      39 45 66 208
Balance laws, local      66
Balance laws, master      41
Balance of energy      68
Balance of energy, global law      102
Balance of energy, nonlocal law      103
Balance of mass and inertia      67
Balance of moment of momentum      12 13 15
Balance of momentum      12 13 15 67 222
Banach space      216
Blood      3
Bochner's theorem      97
Body force, dissipative, nonlocal      145
Body force, external      91
Body force, nonlocal      94
Body force, recoverable, nonlocal      142
Born — von Karman model      248
boundary conditions      59
Boundary data, inhomogeneous      115
Bounded support      40
Brillouin zone      207 248
Carrier fields      108
Carrier fields, boundary conditions for      109
Carrier fields, field equations for      111
Carrier fields, initial data      112
Carrier fields, nonlocal field equations for      117
Carrier fields, terminal data      112
Carrier fields, variational principle for      109
Cauchy data      59 62
Cauchy deformation tensor      9
Cause set      215
Characteristic length      233
Characteristics      205
Clausius — Duhem inequality      36 60 214
Clausius — Duhem inequality, nonlocal      171
Compatibility conditions      11
COMPOSITES      3
Conservation of energy      12—15
Conservation of mass      12—14
Conservation of microinertia      12 13 15
Constitutive equation      17 56 61 255
Constitutive functionals      223 254
Constitutive relations, admissible      176 ff.
Constitutive relations, nonlocal      155 ff. 177
Constitutive relations, variational formulation      199 ff.
Constitutive theory      47
Cosserat deformation tensor      8 215
Cosserat deformation tensor, relative      10
Couple residuals      257
Cracks      206
Deformation tensors      36
Density of spin      211
Density of surface stress      246
Density of surface tension      260
Density of tension      265
Determinism, simplistic      133
Dispersion curves      249
Displacement field      235
Dissipation potential, definition of      178
Dissipation potential, existence of      179
Dissipative nonlocal body force      145
Dissipative stress tensor      30 145
Dissipative stresses      60
Distributions      40
Energy      16 43 213
Energy balance      222
Energy density, internal      68
Energy moments      68
Energy source      43
Energy, balance of      68
Energy, conservation of      12—15
Energy, free      69 214 242 264
Energy, internal      43
Energy, strain      239 243
Energy, surface      43
entropy      16 213 259 see "Global
Entropy balance      153 ff.
Entropy inequality      14 15 61 68 222 228
Entropy production      153 ff.
Entropy residual      226
Equipresence, axiom of      217
Equivalence class of external Cauchy stress tensors      92
Equivalence class of external heat flux vectors      102
Equivalence class of external Piola — Kirchhoff stress tensors      92
Equivalence class of global linear momentum balance laws      93
Equivalence class of laws of balance of energy      103
Equivalence class of laws of balance of moment of momentum      100
Equivalence class of local laws      84
Equivalence class of mass conservation laws      88
Euler — Lagrange equations      111
Euler — Lagrange equations, inhomogeneous      115
Field equations      27 235 245 262
Fluxes, thermodynamic      155
Forces, thermodynamic      155
Fracture      206
Fracture criteria      207 249
Fracture toughness      207
Frechet derivative      218 219
Free energy      69 214 242 264
Free entropy flux      214
Function space      216
Functional      17 217 238 see
Functional arguments of internal energy function      136
Functional decomposition theorem      167 ff.
Functional, response      21 47 50
Galilean invariance      216 220 223 227 238 255
Galilean transformation      216
Gateaux derivative      139
Gaussian coordinates      264
Gibbs equation, nonlocal      137
Global entropy production      227
Global law of balance of charge      106
Global law of balance of energy      102
Global law, definition of      83 ff.
Global law, localization of      84
Global stability      234
Global thermodynamics      137 ff.
Gravitational attraction      246
Green deformation tensor      8 35
Gyration tensor      6 35
Gyration vector      211
Hall current      106
Heat flux vector, equivalence class of      102
Heat flux vector, external      102
Heat supply, external      101
Heat vector      68
Helmholtz free energy      15
Hidden variables in nonlocal thermodynamics      140
Higher-order micromorphic continua      63
Hilbert space      216 251
Homogeneous      18 57
Homogeneous bodies      23
Impenetrability, axiom of      210
Inertia      16
Inertia tensor      67
Infinitesimal deformations      25
Influence function      218
Initial conditions      32 59
Initial data, inhomogeneous      115
Inner structure      40
Integrodifferential equations for carrier fields      112
Internal dissipation      23
Internal energy      43
Internal energy density      68
Internal energy function, local      136
Intrinsic angular momentum      13
Invariance      see also "Galilean invariance" "Rotational
Invariance for nonlocal variational principles      124 ff.
Invariance under rigid body motions      146 ff.
Invariants      60
Inverse micromotion      64
Isotropic elastic bodies      52
Isotropic materials      57 231 234 244
Isotropic simple solid      20
Isotropic solids      54 241
Isotropic tensors      57 260
Isotropy group      19 48
Jump conditions      41
Kinematics      33 63
Lattice dynamics      206 249
Law of Entropy      12 44
Lengths      205 see "Wavelength"
Linear isotropic solids      27 57
Linear momentum, equivalence class of global statements      93
Linear momentum, global balance of      92
Linear momentum, nonlocal law of      94
Linear nonlocality      238 259
Linear theory      25 244
Linear theory of microelasticity      55
Liquid crystals      3 32
Local balance laws      66
Local energy      44
Local entropy production, local negative values of      162
Local Euler — Lagrange operator      116
Local internal energy function      136
Local law, definition of      83
Local law, equivalence class of      84
Local mass closure      133
Local material moduli      233
Local moduli      260 261
Locality, axiom of      209 210
Localization residual for balance of energy      103
Localization residual for balance of moment of momentum      100
Localization residual for mass conservation      87
Localization residual, definition of      85
Macrocrack      206
Macroscopic equations of first kind      118
Macroscopic equations of second kind      119
Macroscopic equations, distributional form of      122
Macroscopic formulations      117
Magnetic flux      106
Mass      15 42 212
Mass conservation, nonlocal      87
Master balance laws      41
Material derivative      7
Material inertia tensor      12
Material moduli      58
Material particle      34
Material surface      210
Material volume      210
Maxwell relations, nonlocal      179
Memory-dependent fluids      63
Memory-dependent materials      33
Microbody force density      67
Microdeformation      12
Microdeformation functions      64
Microdeformation tensor      36
Microdeformation vectors      209
Microelasticity      53
Microelements      39 46 63
Microinertia      4 43 210 212
Microinertia tensor      211 263
Microinertia, spatial      45
Microisotropy      59 263
Micromorphic      3
Micromorphic continua      33
Micromorphic continuum      33 64
Micromorphic continuum of grade one      42
Micromorphic elastic solids      69
Micromorphic elasticity      69
Micromorphic materials      47
Micromorphic medium      34 38
Micromorphic simple fluid      50
Micromorphic theory      19 207
Micromorphic viscous fluid      38
Micromotion      5 6 36 64
Micromotion tensor      7
Micromotion, relative      7 35
Micropolar      3
Micropolar bodies      33 209
Micropolar continua      4
Micropolar continuum      210
Micropolar elastic materials      21
Micropolar elasticity      5 24
Micropolar fluid dynamics      29
Micropolar fluids      207
Micropolar fluids, differential type      10
Micropolar materials      208
Micropolar materials, simple      18
Micropolar viscoelasticity      32
Micropolar viscous fluid of grade N      21
Micropressure tensor      60
Microrotation field      235
Microrotation vector      236
Microstretch      37
Microsurface tractions      67
Microviscoelastic materials      63
Moment of momentum      16 213
Moment of momentum, balance of      12 13 15
Moment of momentum, global balance of      100
Moment tensors      66
Momenta      43
Momentum      16 213 see
Momentum, balance of      12 13 15 67
Momentum, intrinsic angular      13
Natural state      37
Nondissipative fluxes      179
Nonholonomic      11
Nonlinear macroscopic operators      116
Nonlocal body force      94 247
Nonlocal body force and surface tension      96 ff.
Nonlocal body force, recoverable      142
Nonlocal Clausius — Duhem inequality      171
Nonlocal constitutive equations      249
Nonlocal constitutive moduli      230
Nonlocal constitutive relations      151 ff. 165 177
Nonlocal continuum      208
Nonlocal continuum physics      212
Nonlocal dielectric      191
Nonlocal effects      246
Nonlocal elastic solids      207 250
Nonlocal elasticity      206 207 236 237
Nonlocal electromagnetic continua      207
Nonlocal Euler equations      117
Nonlocal Euler — Lagrange operator      117
Nonlocal fluid dynamics      263
Nonlocal fluidic bodies      188
Nonlocal fluids      251
Nonlocal force      231
Nonlocal Gibbs equation      137
Nonlocal laws of balance of energy      103
Nonlocal laws of balance of linear momentum      94
Nonlocal laws of balance of mass      87 89
Nonlocal laws of balance of moment of momentum      100
Nonlocal laws, definition of      83 ff.
Nonlocal mass conservation      87
Nonlocal Maxwell relations      179
Nonlocal micropolar continua      209
Nonlocal micropolar elastic solids      207 217
Nonlocal micropolar elasticity      228
Nonlocal micropolar fluid      208 250 258
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