Symmetric Cauchy stress tensor, 244
Symmetric tensors, 345
Symmetric unimodular tensor, 362
T
Temperature dependent, 373
Temperature gradient diffusion driving force,
402, 403
Tensile stress, 65, 404
Tension-compression cyclic loading, 195
Tensorial variables, 362
Tetrahedron, 15, 16
Theory of gases, 180
Thermal conductivity tensor, 420
Thermal damage, 390
Thermal dissipation, 372
Thermal gradient, 397
Thermodynamic chambers, 75
Thermodynamic forces, 105, 106, 216, 227
Thermodynamic fundamental equation
balance equation, 213
conservation laws (see Conservation laws)
entropy, 215
entropy source, 214
force, 216
Gibbs relation, 215
irreversible fluxes, 216
isolated/closed system, 214
probability and statistics, 215
second law, 215
thermal equilibrium, 215
Thermodynamic potential
dissipation potential, 106
dissipation power and onsager reciprocal
relations, 109–112
forces, 105
formulation, 101–105
intrinsic and thermal dissipation decoupling,
108
time independent dissipation, 108
variables (see Thermodynamic variables)
Thermodynamic restrictions
Cauchy’s stress, 356
defect energy, 352
deformed configuration, 353
dual-mechanism elastic-viscoplastic
constitutive model, 358
elastic symmetric Mandel stress, 357
Helmholtz free energy, 352, 353, 359
intermediate configuration, 354
intermolecular mechanism, 352
irreversible entropy, 359
molecular network mechanism, 352
multi-mechanism generalization, 352
Piola-Kirchhoff stress tensor, 358
plastic stretch rate, 357
reference configuration, 353
specific entropy, 359
stress measures, 354, 357
stress tensor, 355
surface tractions, 355
transformation rules, 354
velocity gradient, 357
virtual work rate, 353
Thermodynamic state index (TSI), 232, 324,
329, 335, 336, 411, 418, 421, 423
Boltzmann equation, 192
computational mechanics, 194
definition, 193
degradation, energy storage capacity, 193,
194
disorder parameter, 191
entropy, 133, 191, 194
fundamental equation, 191
gas constant, 192
laws of thermodynamics, 193
material, 192
monotonic loading test, 195–197
one-dimensional spring, 193
plastic deformation, 194
properties, 195
ramification, 194
second law of thermodynamics, 191
specimen dimensions, 195
statistical mechanics, 191
strain energy, 193
tension-compression cyclic loading, 195
TSI axis, 191
Thermodynamic variables
appropriate choice, 100
microstate, 100
Newton’s laws of motion, 100
observable, 100
Thermodynamics
Boltzmann distribution, 132
classical irreversible, 116
continuum mechanics, 2
continuum system, 73
corrosion-fatigue volumetric entropy, 129
elastic, 122
endochronic plasticity theory, 118
engineering mechanics, 116
entropy (see Entropy)
equilibrium, 74–75, 127
equilibrium vacancy, 407
Index
439
Symmetric tensors, 345
Symmetric unimodular tensor, 362
T
Temperature dependent, 373
Temperature gradient diffusion driving force,
402, 403
Tensile stress, 65, 404
Tension-compression cyclic loading, 195
Tensorial variables, 362
Tetrahedron, 15, 16
Theory of gases, 180
Thermal conductivity tensor, 420
Thermal damage, 390
Thermal dissipation, 372
Thermal gradient, 397
Thermodynamic chambers, 75
Thermodynamic forces, 105, 106, 216, 227
Thermodynamic fundamental equation
balance equation, 213
conservation laws (see Conservation laws)
entropy, 215
entropy source, 214
force, 216
Gibbs relation, 215
irreversible fluxes, 216
isolated/closed system, 214
probability and statistics, 215
second law, 215
thermal equilibrium, 215
Thermodynamic potential
dissipation potential, 106
dissipation power and onsager reciprocal
relations, 109–112
forces, 105
formulation, 101–105
intrinsic and thermal dissipation decoupling,
108
time independent dissipation, 108
variables (see Thermodynamic variables)
Thermodynamic restrictions
Cauchy’s stress, 356
defect energy, 352
deformed configuration, 353
dual-mechanism elastic-viscoplastic
constitutive model, 358
elastic symmetric Mandel stress, 357
Helmholtz free energy, 352, 353, 359
intermediate configuration, 354
intermolecular mechanism, 352
irreversible entropy, 359
molecular network mechanism, 352
multi-mechanism generalization, 352
Piola-Kirchhoff stress tensor, 358
plastic stretch rate, 357
reference configuration, 353
specific entropy, 359
stress measures, 354, 357
stress tensor, 355
surface tractions, 355
transformation rules, 354
velocity gradient, 357
virtual work rate, 353
Thermodynamic state index (TSI), 232, 324,
329, 335, 336, 411, 418, 421, 423
Boltzmann equation, 192
computational mechanics, 194
definition, 193
degradation, energy storage capacity, 193,
194
disorder parameter, 191
entropy, 133, 191, 194
fundamental equation, 191
gas constant, 192
laws of thermodynamics, 193
material, 192
monotonic loading test, 195–197
one-dimensional spring, 193
plastic deformation, 194
properties, 195
ramification, 194
second law of thermodynamics, 191
specimen dimensions, 195
statistical mechanics, 191
strain energy, 193
tension-compression cyclic loading, 195
TSI axis, 191
Thermodynamic variables
appropriate choice, 100
microstate, 100
Newton’s laws of motion, 100
observable, 100
Thermodynamics
Boltzmann distribution, 132
classical irreversible, 116
continuum mechanics, 2
continuum system, 73
corrosion-fatigue volumetric entropy, 129
elastic, 122
endochronic plasticity theory, 118
engineering mechanics, 116
entropy (see Entropy)
equilibrium, 74–75, 127
equilibrium vacancy, 407
Index
439