Newtonian mechanics, 229, 231
non-recoverable energy, 231
plastic work dissipation, 232
small strain formulation, 229
straining process, 233
stress and strain tensor, 229
temperature distribution, 232
temperature thermomigration, 233
Function of the intrinsic parameters of the
system, 83
Fundamental equation, 89
Fundamental relation, 83, 84, 87, 90, 99, 100
G
Gauss integration point, 411
Gauss’s theorem, 217, 221
General couple stress theory
constitutive relationships, 253
finite element discretization, 253
independent degrees of freedom, 252
Lagrange multiplier formulation, 254, 255
pure displacement formulation, 253, 254
General return-mapping algorithm
elastic consistent tangent moduli, 325
finite element formulation, 329
internal heat source, 325
irreversible entropy generation, 325
isotropic hardening modulus, 326
iterations, 324
residual functions, 327
systematic application, 329
unconditionally stable, 329
viscoplastic strain, 329
General systems theory, 117, 130
Generalized coordinates, 161
Generalized couple stress theory, 238
Generalized irreversible forces X and fluxes J,
110
Generalized self-consistent scheme (GSCS),
310
Generalized standard materials, 107
Gent free energy, 368
Gibbs-Duhem relation, 85–89
Gibbs relation, 226
Glass-rubber transition, 374, 378
Glass transition temperature, 366
Gravity, 12
Green deformation tensor, 49–52
Green’s function, 281, 285
H
Hardening-softening behavior, 367, 376
Heat conduction, 371
Heat exchange, 91, 371
Heat flux, 352
Heat transfer, 397, 412–415
Helmholtz free energy, 103, 226, 230, 266,
351–353, 359, 370, 418
Helmholtz free energy density, 361
Helmholtz free energy function, 362
Helmholtz free specific energy, 101, 104
High temperature mechanics, 365, 373, 378
Hofstadter lattice, 127
Homogeneity, 2
Homogenization, 277
Hooke’s law, 203
Hydrostatic stress, 26, 27
Hydrostatic tensor, 26
I
Imaginary point, 16, 17
Incompressible materials, 65
Independent plasticity, 206
Independent variables, 87, 99
Indeterminate couple stress theory, 238
Integral equation, 282
Intensive parameters, 86, 88, 89
Intensive variable
definition, 82
Intermediate (relaxed) configurations, 346
Intermediate configuration, 354
Intermolecular mechanism, 352
Intermolecular network mechanism, 380
Intermolecular resistance
amorphous polymers, 363
Arrhenius-type temperature dependence,
363
Cauchy stress tensor, 361
characteristic viscoplastic shear strain rates,
365
dislocation and dislocation motion, 363
dual-mechanism model, 366
elastic logarithmic strain, 361, 362
elastic Mandel stress, 362
Helmholtz free energy, 361
Helmholtz free energy density, 361
Kinematic hardening, 362
material properties, 365
non-isothermal loading, 365
order parameter, 365
Piola-Kirchhoff stress tensor, 361
plastic deformation gradient, 363, 365
plastic flow, 364
plastic flow resistance, 364
plastic stretch rate, 362
Richeton’s model, 366
stretch-like internal variable, 362
Index
433
non-recoverable energy, 231
plastic work dissipation, 232
small strain formulation, 229
straining process, 233
stress and strain tensor, 229
temperature distribution, 232
temperature thermomigration, 233
Function of the intrinsic parameters of the
system, 83
Fundamental equation, 89
Fundamental relation, 83, 84, 87, 90, 99, 100
G
Gauss integration point, 411
Gauss’s theorem, 217, 221
General couple stress theory
constitutive relationships, 253
finite element discretization, 253
independent degrees of freedom, 252
Lagrange multiplier formulation, 254, 255
pure displacement formulation, 253, 254
General return-mapping algorithm
elastic consistent tangent moduli, 325
finite element formulation, 329
internal heat source, 325
irreversible entropy generation, 325
isotropic hardening modulus, 326
iterations, 324
residual functions, 327
systematic application, 329
unconditionally stable, 329
viscoplastic strain, 329
General systems theory, 117, 130
Generalized coordinates, 161
Generalized couple stress theory, 238
Generalized irreversible forces X and fluxes J,
110
Generalized self-consistent scheme (GSCS),
310
Generalized standard materials, 107
Gent free energy, 368
Gibbs-Duhem relation, 85–89
Gibbs relation, 226
Glass-rubber transition, 374, 378
Glass transition temperature, 366
Gravity, 12
Green deformation tensor, 49–52
Green’s function, 281, 285
H
Hardening-softening behavior, 367, 376
Heat conduction, 371
Heat exchange, 91, 371
Heat flux, 352
Heat transfer, 397, 412–415
Helmholtz free energy, 103, 226, 230, 266,
351–353, 359, 370, 418
Helmholtz free energy density, 361
Helmholtz free energy function, 362
Helmholtz free specific energy, 101, 104
High temperature mechanics, 365, 373, 378
Hofstadter lattice, 127
Homogeneity, 2
Homogenization, 277
Hooke’s law, 203
Hydrostatic stress, 26, 27
Hydrostatic tensor, 26
I
Imaginary point, 16, 17
Incompressible materials, 65
Independent plasticity, 206
Independent variables, 87, 99
Indeterminate couple stress theory, 238
Integral equation, 282
Intensive parameters, 86, 88, 89
Intensive variable
definition, 82
Intermediate (relaxed) configurations, 346
Intermediate configuration, 354
Intermolecular mechanism, 352
Intermolecular network mechanism, 380
Intermolecular resistance
amorphous polymers, 363
Arrhenius-type temperature dependence,
363
Cauchy stress tensor, 361
characteristic viscoplastic shear strain rates,
365
dislocation and dislocation motion, 363
dual-mechanism model, 366
elastic logarithmic strain, 361, 362
elastic Mandel stress, 362
Helmholtz free energy, 361
Helmholtz free energy density, 361
Kinematic hardening, 362
material properties, 365
non-isothermal loading, 365
order parameter, 365
Piola-Kirchhoff stress tensor, 361
plastic deformation gradient, 363, 365
plastic flow, 364
plastic flow resistance, 364
plastic stretch rate, 362
Richeton’s model, 366
stretch-like internal variable, 362
Index
433