Effective thermo-mechanical properties (cont.)
interphase layer, 309
numerical examples, 312, 313
Poisson’s ratio, 315
shear modulus, 310–312
theoretical solution, 309
Young modulus, 312
Effective valence, 401
Eigen-strain, 284, 285
Eight-node linear brick elements (C3D8T), 384
Elastic and plastic deformation gradients, 346
Elastic and plastic rotation tensors, 349
Elastic distortional Almansi tensor, 368
Elastic Eigen-strain, 285
Elastic logarithmic strain, 361, 362
Elastic Mandel stress, 358, 361, 362, 369
Elastic modulus, 334, 335, 337, 374
Elastic recovery, 370
Elastic response, 106
Elastic right Cauchy tensor, 361
Elastic shear modulus, 284
Elastic strain energy, 353
Elastic strain rate, 209
Elastic strain-stress constitutive model, 411
Elastic stretch rate tensor, 350
Elastic symmetric Mandel stress, 357
Elastomers, 369
Electric field, 396
Electrical conduction equations, 415, 416
Electrical current, 403
Electrical current density, 400
Electrical field intensity, 412
Electro-magnetic and chemical loads, 80
Electromagnetic radiation theory, 182
Electromigration
Blech’s critical length, 396
Boltzmann constant, 418
characteristics, 405
damage evolution, 395
definition, 396
degradation, conductor, 395
driving forces (see Driving forces of
electromigration)
electron wind forces, 396, 400–405
electron-wind transfer, 395
experiment and simulation result, 423
finite element method, 396, 416
heat transfer, 412–415
material properties, 421, 422
physical mechanism, 395
properties, 396
quantification, 396
second law of thermodynamics, 417
solder joint, 421, 422
solid conductor, 395
stress gradient diffusion driving force,
404–406
temperature gradient diffusion driving force,
402, 403
and thermomigration
diffusion (see Diffusion)
Fick's first law, 399
Fick's second law, 399
mechanical deformation, 397
mechanics, 398
mechanism, 398
microelectronics solder joint, 398
time to failure, 421, 422
TSI, 421, 423
Electron flux density, 396
Electron wind, 401
Electron wind forces, 396, 400–405
Electronics
solder joint, 398
Electron-wind forces, 396, 400
Electron-wind transfer, 395
Electro-thermo-chemical-radiation
mechanisms, 95
Electro-thermo-mechanical loading
application, 3
Endochronic plasticity theory, 118
Endochronic theory, 118
Energetic fundamental relation, 87
Energy conservation, 221–223
Energy conservation law, 79
Energy-versus-momentum, 402
Engineering mechanics, 116
Engineering strain, 45
Ensemble-average stress norm, filler particles
averaged internal stresses, 299
non-interacting solution, 298
positive definite fourth-rank tensor, 300
volume-averaged stress tensor, 299
Ensemble-average stress norm, matrix
alternative expression, 297
components, 297
CTE mismatch, 298
Eigen-strain, 295
far-field stress, 295
macroscopic stress, 296
non-interacting solution, 296
positive definite fourth-rank tensor, 297
Ensemble-averaged loading function, 290
Ensemble-volume averaging process
effective elastic properties, 282
elastic stiffness tensor, 280
430
Index
interphase layer, 309
numerical examples, 312, 313
Poisson’s ratio, 315
shear modulus, 310–312
theoretical solution, 309
Young modulus, 312
Effective valence, 401
Eigen-strain, 284, 285
Eight-node linear brick elements (C3D8T), 384
Elastic and plastic deformation gradients, 346
Elastic and plastic rotation tensors, 349
Elastic distortional Almansi tensor, 368
Elastic Eigen-strain, 285
Elastic logarithmic strain, 361, 362
Elastic Mandel stress, 358, 361, 362, 369
Elastic modulus, 334, 335, 337, 374
Elastic recovery, 370
Elastic response, 106
Elastic right Cauchy tensor, 361
Elastic shear modulus, 284
Elastic strain energy, 353
Elastic strain rate, 209
Elastic strain-stress constitutive model, 411
Elastic stretch rate tensor, 350
Elastic symmetric Mandel stress, 357
Elastomers, 369
Electric field, 396
Electrical conduction equations, 415, 416
Electrical current, 403
Electrical current density, 400
Electrical field intensity, 412
Electro-magnetic and chemical loads, 80
Electromagnetic radiation theory, 182
Electromigration
Blech’s critical length, 396
Boltzmann constant, 418
characteristics, 405
damage evolution, 395
definition, 396
degradation, conductor, 395
driving forces (see Driving forces of
electromigration)
electron wind forces, 396, 400–405
electron-wind transfer, 395
experiment and simulation result, 423
finite element method, 396, 416
heat transfer, 412–415
material properties, 421, 422
physical mechanism, 395
properties, 396
quantification, 396
second law of thermodynamics, 417
solder joint, 421, 422
solid conductor, 395
stress gradient diffusion driving force,
404–406
temperature gradient diffusion driving force,
402, 403
and thermomigration
diffusion (see Diffusion)
Fick's first law, 399
Fick's second law, 399
mechanical deformation, 397
mechanics, 398
mechanism, 398
microelectronics solder joint, 398
time to failure, 421, 422
TSI, 421, 423
Electron flux density, 396
Electron wind, 401
Electron wind forces, 396, 400–405
Electronics
solder joint, 398
Electron-wind forces, 396, 400
Electron-wind transfer, 395
Electro-thermo-chemical-radiation
mechanisms, 95
Electro-thermo-mechanical loading
application, 3
Endochronic plasticity theory, 118
Endochronic theory, 118
Energetic fundamental relation, 87
Energy conservation, 221–223
Energy conservation law, 79
Energy-versus-momentum, 402
Engineering mechanics, 116
Engineering strain, 45
Ensemble-average stress norm, filler particles
averaged internal stresses, 299
non-interacting solution, 298
positive definite fourth-rank tensor, 300
volume-averaged stress tensor, 299
Ensemble-average stress norm, matrix
alternative expression, 297
components, 297
CTE mismatch, 298
Eigen-strain, 295
far-field stress, 295
macroscopic stress, 296
non-interacting solution, 296
positive definite fourth-rank tensor, 297
Ensemble-averaged loading function, 290
Ensemble-volume averaging process
effective elastic properties, 282
elastic stiffness tensor, 280
430
Index