Betten J. — Creep Mechanics :: Электронная библиотека попечительского совета мехмата МГУ

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Betten J. — Creep Mechanics

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Название: Creep Mechanics

Автор: Betten J.

Аннотация:

Provides a short survey of recent advances in the mathematical modelling of the mechanical behavior of anisotropic solids under creep conditions, including principles, methods, and applications of tensor functions. Some examples for practical use are discussed, as well as experiments by the author to test the validity of the modelling. The monograph offers an overview of other experimental investigations in creep mechanics. Rules for specifying irreducible sets of tensor invariants, scalar coefficients in constitutive and evolutional equations, and tensorial interpolation methods are also explained. The second edition includes a CD-ROM containing the examples and algorithms in more detail and the appendant figures in color. The text has been re-examined and improved throughout.

Язык:

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2 edition

Год издания: 2005

Количество страниц: 353

Добавлена в каталог: 12.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$L_{2}$ -error norm      216
$\sqrt{t}$ -law      211 215—216 221
Abel integral equation      309—310
Accelerating creep      51
Activation energy for creep      211
Activation energy for self-diffusion      211
Actual net-stress tensor      127 142
Alternating symbol      11
Anisotropic      3 105 107
Anisotropic damage      130 148—149
Anisotropic damage growth      73
Anisotropic damage state      73 127
Anisotropic damage tensors      3 69 118
Anisotropic hardening      254
Anisotropic materials      101
Anisotropic primary creep      2 53
Anisotropic viscoplastic solids      240
Anisotropy tensor      74
Anomalous flows      186
Arrhenius function      211
Asymmetric effective stress tensor      148
Austenite      242
Austenitic steel      52
Bauschinger effect      60 89
Best approximation      258 317—318
Biaxial specimen      254
Bingham model      238 240
Bivector      73 132—135
Boltzmann’s axiom      44
Boltzmann’s superposition principle      181 187 189 289
bulk modulus      165 168
Bulk viscosity      165—166
Burgers model      229—236
C — S — D effect      115
Canonical form      74 105—106 128—129
Capillar flows      185
Cauchy — Green relative right tensor      183
Cauchy — Green right tensor      36 81 184 194
Cauchy’s equation of motion      47 169
Cauchy’s stress tensor      44 8 72 130 141 147 253
Cauchy’s tetrahedron      73
Cavitation      247
Cavity growth      248
Characteristic equation      14—15 45 124
Characteristic polynomial      119—122
Chi-square distribution      204—205
Christoffel symbols      27—30
Christoffel symbols of the first kind      24 27
Christoffel symbols of the second kind      24 27
Circumferential stresses      87
Classical flow rule      103
Classical normality rule      101
Classical strain tensor      38
Climbing of dislocations      211
Coaxial      148
Collocation method      275
Collocation point      275
Compatibility equations      39
Complementary energy      149
Complementary error function      317
Complex compliance      226 229
complex modulus      226 228
Complex parameters      226 228
Complex shear modulus      226
Complex shear viscosity      227
Complex viscosity      226 229
Compliance      197
Compressible fluids      170
Computer algebra systems      322
Condition of form invariance      111
Conditions of compatibility      109
Conjugate variables      48
Constitutive equations      31 48 1—9 111 131 231 245—248
Continuous transition      278
Continuum Damage Mechanics      3
Continuum mechanics      31
contravariance      17
Contravariant base      22—23
Contravariant base vectors      19
Contravariant components      17 22 36
Contravariant metric tensors      20
Contravariant tensor components      29
Convection rate of change      34
Convective rate      170
Convective stress rate      174
Convexity      241
Convolution      191—192 289 301
Convolution integral      289
Convolution theorem      191—192 290—293 295 298 301
Convolution type      300
Cosserat continuum      41 44
COUETTE-flow      185
Couple stresses      47
Couple-stress vector      41
Covariance      17
Covariant base vectors      19
Covariant basis      19 23
Covariant components      17 22 36
Covariant derivatives      25
Covariant metric tensors      20
Covariant tensor components      29
Creep behavior      229
Creep behavior of concrete      207
Creep buckling      2 53
Creep condition      56 113 117 245—246
Creep criterion      111
Creep curve      50
Creep curves for concrete      209—210
Creep damage      3 69
Creep function      188—191 193 195—196 198 201 203 205 207 216 231 295 301
Creep integral      190
Creep mechanics      1 51 316
Creep potential      2 53 55—57 61 63 72 101—102 108
Creep potential hypothesis      2 52—53 101 105—107
Creep relation      188
Creep response      190
Creep spectra      205 207
Creep strain      211
Creep tensor      188
Creep velocity potential      2
Creep-failure      100
Creep-strength-differential effect      114 115
Cubic splines      259
Curve fitting      258
Curvlinear coordinates      16
Cylindrical coordinates      29
Damage effective stress      131 147 149
Damage effective tensor      148 150
Damage equivalence hypothesis      150
Damage equivalence principles      149
Damage isotropy principle      150
Damage mechanics      3—4
Damage state      246
Damage tensor      3 72 74 107 118 131 136
Damage variables      148
Damaged continuum      133 135 141
Damaged materials      107
Damped free vibration      225
Damping factor      225 279
Damping rule      286
Deflection curve      297 299—300
Deformation gradient      174 194
Del operator      23
Deviator      14
Deviatoric      110 115
Die swell      186
Differentiation of the transform      287
Diffusion coefficient      212
Diffusion controlled process      211 316
Diffusion equation      316

Diffusion way      215
Diffusional creep      211
Dirac function      189 274 276 280 294 296
Discrete relaxation spectrum      219
Discrete retardation spectrum      197 198
Dislocation creep      211 248 254
Displacement vector      34
Dissipation power      166
Dissipative energy      225
Dissipative force      224
Dissipative stress      224
Distortion      14 166
Divergence of a vector field      23
Divergence theorem of Gauss      45
Double tensor      79
Dual basis      19
Dual damage tensor      136
Dual tensor of continuity      136
Dyadic product      25
Dynamic shear modulus      227
Dynamic shear viscosity      227
d’Alembert’s principle      46
Effective stress tensor      147 150
Eigenfrequency      225
Eigenvalue problem      120 123—124
Eigenvalues      45
Eigenvectors      45
Elastic solids      187
Elastoviscoplastic      237
Elementary symmetric functions      15
Elliptical hysteresis      225
Energy dissipation      223
Equation of state      163
Equations of equilibrium      26 28 46
Equivalent creep strain      83
Equivalent stresses      98
Euclidean space      16 49
Eulerian coordinates      33
EULERian finite strain tensor      37 175—176
EULERian infinitesimal strain tensor      38
Euler’s theorem on homogeneous functions      57
Evolution of damage      256—258
Evolutional equations      127 245
Experimental foundations of solid mechanics      245
Extension flow      167
Extension viscosity      167 195
External variables      230
Extra stress tensor      163
Fading memory      181—182 185 194
Failure time      98
Finite theory of elasticity      47
Finite-strain theory      38 100
First Piola — Kirchhoff stress tensor      47 178
Flow potential      53
Flow rule      56
Fourth-order constitutive tensor      73
Fourth-order damage tensors      131
Fourth-order material tensor      124
Fourth-order permutation tensor      125
Fourth-order symmetric tensor      125
Fourth-order tensor      15 110 130
Fredholm integral equation      300
Frequency ratio      279
Gamma distribution      199
Gamma function      199 283
Gauss distribution      278
GAUSS error functional      2— 213 317—322
Generalized creep function      197
Generalized relaxation function      218
Geometrical non-linearities      38
Gradient of a vector      25
Grain boundary cavitation      248
Grain boundary diffusion      247
Growth mechanisms      247
Hamilton — Cayley theorem      15 61 111 152—153 173
Hardening of aluminium alloy      264 266
Harmonic loading      223 229
Heaviside function      86 196 231—234 271—274 276 294
Hencky equation      244
Hencky’s strain tensor      81 100
Hereditary integral      181 187—190 289
HlLL-condition      60
HOOKE element      196 218
Hypothesis of the equivalent dissipation rate      57 156 239
Hysteresis      223—226
Hysteresis loop      223
Ideal material response      49
Impulse function      278
Incompatibility tensor      39
Incompressibility      242
Incompressible Newton fluid      166
Index notation      9
Inertial force      46 170
Initial anisotropy      73 127 131
Integral equation      281 300—306
Integrity basis      29 101 104 108 110—112 114 123 128 157
Integro differential equation      311
Intergranular creep fracture      71 247
Internal variables      230 243
Interpolation methods for tensor functions      127 151—152
Invariant damage models      150
Invariant forms      150
Inverse Laplace transform      207 285
Irreducible invariants      14 15 28—29 45 127 157—158
Irreducible tensor-generators      126
Isochoric      82
Isochoric distortion      38
Isotropic      2 106 140
Isotropic creep potential      55
Isotropic material      73
Isotropic tensor function      150 172
Jaumann derivative      72 127
Jaumann stress rate      173
Joint invariants      111
Kelvin creep function      302
Kelvin elements      196
Kelvin model      194 197 217 228—229 294 296 302
Kelvin solid      189
Kernel function      182 301
Kinetic equation      70
Kohlrausch function      222
Kronecker tensor      20
Lagrange finite strain tensor      36—37 48 174
Lagrange infinitesimal strain tensor      38
Lagrange multiplier method      123—124
Lagrange’s multiplier      56
Lagrangian coordinates      33
Lame constants      120
Laplace operator      25 28
Laplace parameter      228—229
Laplace transform      190 199 219—220 228 281 284 292 294 296 302 312 314—315
Laplace transform of an integral      288
Laplace transform pairs      323—329
Laplace transformation      199 281 284 292 313
Least squares curve fitting      259—260
Lehr’s damping measure      225
Limiting creep stresses      115
Linear functional      182 185 194
Linear operator      15 44
Linear standard solid model      217
Linear transformation      13 54 148
Linear viscoelastic      190
Linear viscous fluids      163
Linearity rule      315
Local rate      170
Local rate of change      34
Logarithmic strain tensor      37—38 82
Longitudinal stresses      87
Loss angle      224
Loss compliance      226

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