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