general couple stress theory, 238
linear elastic behavior, 238
micro rotation, 239
rotation vector, 238
strain and curvatures, 239
symmetric/anti-symmetric components, 240
traction vector, 240
Couple stress, 20, 21
Coupled thermo-mechanical loading, 371
Critical entropy level, 372
Current density
and temperature gradient, 395
blocking boundary conditions, 405
conductor, 405
definition, 415
electrical, 400
electron flux density, 396
electron-wind transfer, 395
mechanics based, 396
product, 406
thermomigration, 402
Cyclic loading
stress-strain diagram, 195–197
TSI, 196
Cyclic stress-strain response, 337, 338, 340
D
Defect energy, 352
Deformable bodies, 11
Deformation gradient, 349
Deformation gradient tensor, 220
Deformation tensor, 420
Degradation evolution, 322
Deviatoric stress tensor, 26–28
Diffusion
activation energy, 399
atomic, 398
electron flow assisted diffusion process, 406
irreversible mass diffusion mechanisms,
395
mass transport, 396
non-steady state, 399, 400
salt-water system, 398
stress gradient, 404–406
temperature gradient, 402–404
vacancy, 397, 409
Direction cosines, 16–18, 23, 24
Disorder, 96–99
Disordered state, 96
Dissipated energy, 353
Dissipation function, 106, 111
Dissipation potential, 106
Dissipation power, 109–112
Dissipation variables, 107
Dissipative resistance, 370
Divergence theorem, 63, 79, 413, 415
Driving forces of electromigration
atomic vacancy, 397
electric field, 396
stress gradient, 397
thermal gradient, 397
Driving stress, 362
Dual- and trial-mechanism models, 360
Dual-mechanism constitutive models, 360
Dual-mechanism model, 365, 366
Dual-mechanism viscoplastic model
elastic and plastic deformation gradients,
383
frame-indifference, 383
numerical integration, 384
plastic stretch rate tensors, 384
PMMA
isothermal stretching, 384–390
non-isothermal stretching, 390–391
rate dependency, 383
staggered method, 381
E
Effective bulk modulus, 310
Effective charge, 401
definition, 401
vs. temperature relation, 402
Effective coefficient of thermal expansion
(ECTE), 310
Effective nuclear charge, 401
Effective shear modulus, 310–312
Effective stress concept
back-stress, 209
continuous state variables, 208
incremental procedure, 208
micro-cracks/micro-cavities, 207
nominal uniaxial, 207
RVE, 207, 208
strain equivalence principle, 208
tangential constitutive tensor, 208
thermodynamics state index space, 209
UMT strain energy density, 208
Effective thermo-mechanical properties
analytical and numerical evaluation, 313
bulk modulus, 310, 315
CSA, 309
ECTE, 310
filler and matrix, 309
imperfect interface bond, 309
Index
429
linear elastic behavior, 238
micro rotation, 239
rotation vector, 238
strain and curvatures, 239
symmetric/anti-symmetric components, 240
traction vector, 240
Couple stress, 20, 21
Coupled thermo-mechanical loading, 371
Critical entropy level, 372
Current density
and temperature gradient, 395
blocking boundary conditions, 405
conductor, 405
definition, 415
electrical, 400
electron flux density, 396
electron-wind transfer, 395
mechanics based, 396
product, 406
thermomigration, 402
Cyclic loading
stress-strain diagram, 195–197
TSI, 196
Cyclic stress-strain response, 337, 338, 340
D
Defect energy, 352
Deformable bodies, 11
Deformation gradient, 349
Deformation gradient tensor, 220
Deformation tensor, 420
Degradation evolution, 322
Deviatoric stress tensor, 26–28
Diffusion
activation energy, 399
atomic, 398
electron flow assisted diffusion process, 406
irreversible mass diffusion mechanisms,
395
mass transport, 396
non-steady state, 399, 400
salt-water system, 398
stress gradient, 404–406
temperature gradient, 402–404
vacancy, 397, 409
Direction cosines, 16–18, 23, 24
Disorder, 96–99
Disordered state, 96
Dissipated energy, 353
Dissipation function, 106, 111
Dissipation potential, 106
Dissipation power, 109–112
Dissipation variables, 107
Dissipative resistance, 370
Divergence theorem, 63, 79, 413, 415
Driving forces of electromigration
atomic vacancy, 397
electric field, 396
stress gradient, 397
thermal gradient, 397
Driving stress, 362
Dual- and trial-mechanism models, 360
Dual-mechanism constitutive models, 360
Dual-mechanism model, 365, 366
Dual-mechanism viscoplastic model
elastic and plastic deformation gradients,
383
frame-indifference, 383
numerical integration, 384
plastic stretch rate tensors, 384
PMMA
isothermal stretching, 384–390
non-isothermal stretching, 390–391
rate dependency, 383
staggered method, 381
E
Effective bulk modulus, 310
Effective charge, 401
definition, 401
vs. temperature relation, 402
Effective coefficient of thermal expansion
(ECTE), 310
Effective nuclear charge, 401
Effective shear modulus, 310–312
Effective stress concept
back-stress, 209
continuous state variables, 208
incremental procedure, 208
micro-cracks/micro-cavities, 207
nominal uniaxial, 207
RVE, 207, 208
strain equivalence principle, 208
tangential constitutive tensor, 208
thermodynamics state index space, 209
UMT strain energy density, 208
Effective thermo-mechanical properties
analytical and numerical evaluation, 313
bulk modulus, 310, 315
CSA, 309
ECTE, 310
filler and matrix, 309
imperfect interface bond, 309
Index
429