Thermodynamics (cont.)
equilibrium/diffusion-driving force, 398
fatigue, 119
fatigue crack nucleation, 128
FFE, 128, 129
first law, 75–80, 351
flow potential, 122
fluctuation theorem, 127
fluxes, 116
forces, 119–121, 126
fracture, 128
fundamental equation, 396
general systems theory, 117, 130
internal energy, 125
irreversible entropy generation rate, 131
irreversible processes, classical theory, 122
Lagrangian mechanics, 115
LEDs, 131
macroscopic scale, 73
Mechano-Thermodynamics theory, 129,
130
modeling mechanics, 124
Newtonian mechanics, 73, 115, 124
number of cycles to failure vs. FFE, 128
phenomenological curve fitting methods,
115
Prigogine, 116
Prigogine’s dissipative structure theory, 117
principle, 419
probabilistic model, 124
pseudo-thermodynamics forces, 120
Rayleigh-Bénard instability, 116
rice, 118, 119, 121–124
second law, 119, 351
self-organization, 117
stability, 351
surface stress vector, 123
thermal conductivity, 125
tribo-fatigue entropy, 129, 130
TSI, 411, 418, 421
variables, 127
yield surface, 119
Thermodynamics equilibrium, 74–75
Thermodynamics Gibbs relation, 215
Thermodynamics state index (TSI), 94,
371–373
Boltzmann equation, 135
entropy, 136
materials, 135
Mechanical theory of heat (see Mechanical
theory of heat)
non-equilibrium states, 137
permutability measure, 136, 137
space-time coordinate system, 134
statistical mechanics, 135, 136
Thermo-elastic effect, 371
Thermo-elastic laws, 105
Thermo-elastic materials, 105
Thermo-mechanical analysis, 3
Thermo-mechanical constitutive model, 233
Thermo-mechanical loading, 106, 373, 390
Thermomigration, 233
and electromigration (see Electromigration)
diffusion driving force, 397
electrical current, 395
external stress gradients, 397
intrinsic part, 403
Joule heating, 395
material degradation process, 395
principal, 395
Thermos-electro-mechanical-chemicalradiation processes, 95
Thermos-mechanical loading, 233
Third law of thermodynamics, 84
Third law of unified mechanics theory, 134
Three-phase composites, non-interacting
solution
elastic moduli, 301
ensemble-average stress norm, matrix
algebra, 303
alternative expression, 305
CTE mismatch, 306
Eigen-strain, 302
Eshelby theory, 302
loading function, 304
macroscopic stress, 304
perturbations, 302
plastic strain, 302
positive definite fourth-rank tensor, 303
probability density functions, 303
q-phase inhomogeneity, 302
ensemble-average stress, filler particles
average internal stress, 307
definite fourth-rank tensor, 308
eigen-strain, 306
forms, 306
volume-averaged stress tensor, 307
spherical voids, 300
Time independent dissipation (instantaneous
dissipation), 108
Toupin-Mindlin higher order stress theory
displacement gradients, 242
elastic strain gradients, 244
Lamè constants, 244
strain-displacement kinematic relations, 244
symmetric Cauchy stress tensor, 244
440
Index
equilibrium/diffusion-driving force, 398
fatigue, 119
fatigue crack nucleation, 128
FFE, 128, 129
first law, 75–80, 351
flow potential, 122
fluctuation theorem, 127
fluxes, 116
forces, 119–121, 126
fracture, 128
fundamental equation, 396
general systems theory, 117, 130
internal energy, 125
irreversible entropy generation rate, 131
irreversible processes, classical theory, 122
Lagrangian mechanics, 115
LEDs, 131
macroscopic scale, 73
Mechano-Thermodynamics theory, 129,
130
modeling mechanics, 124
Newtonian mechanics, 73, 115, 124
number of cycles to failure vs. FFE, 128
phenomenological curve fitting methods,
115
Prigogine, 116
Prigogine’s dissipative structure theory, 117
principle, 419
probabilistic model, 124
pseudo-thermodynamics forces, 120
Rayleigh-Bénard instability, 116
rice, 118, 119, 121–124
second law, 119, 351
self-organization, 117
stability, 351
surface stress vector, 123
thermal conductivity, 125
tribo-fatigue entropy, 129, 130
TSI, 411, 418, 421
variables, 127
yield surface, 119
Thermodynamics equilibrium, 74–75
Thermodynamics Gibbs relation, 215
Thermodynamics state index (TSI), 94,
371–373
Boltzmann equation, 135
entropy, 136
materials, 135
Mechanical theory of heat (see Mechanical
theory of heat)
non-equilibrium states, 137
permutability measure, 136, 137
space-time coordinate system, 134
statistical mechanics, 135, 136
Thermo-elastic effect, 371
Thermo-elastic laws, 105
Thermo-elastic materials, 105
Thermo-mechanical analysis, 3
Thermo-mechanical constitutive model, 233
Thermo-mechanical loading, 106, 373, 390
Thermomigration, 233
and electromigration (see Electromigration)
diffusion driving force, 397
electrical current, 395
external stress gradients, 397
intrinsic part, 403
Joule heating, 395
material degradation process, 395
principal, 395
Thermos-electro-mechanical-chemicalradiation processes, 95
Thermos-mechanical loading, 233
Third law of thermodynamics, 84
Third law of unified mechanics theory, 134
Three-phase composites, non-interacting
solution
elastic moduli, 301
ensemble-average stress norm, matrix
algebra, 303
alternative expression, 305
CTE mismatch, 306
Eigen-strain, 302
Eshelby theory, 302
loading function, 304
macroscopic stress, 304
perturbations, 302
plastic strain, 302
positive definite fourth-rank tensor, 303
probability density functions, 303
q-phase inhomogeneity, 302
ensemble-average stress, filler particles
average internal stress, 307
definite fourth-rank tensor, 308
eigen-strain, 306
forms, 306
volume-averaged stress tensor, 307
spherical voids, 300
Time independent dissipation (instantaneous
dissipation), 108
Toupin-Mindlin higher order stress theory
displacement gradients, 242
elastic strain gradients, 244
Lamè constants, 244
strain-displacement kinematic relations, 244
symmetric Cauchy stress tensor, 244
440
Index