Index
A
ABAQUS model, 387
ABAQUS simulation, 388
Action-reaction law, 10
Activation energy, 366, 379, 380
Activation volume, 380
Almansi tensor, 348, 349
Al thin film strips, 404
Alumina trihydrate (ATH), 278, 279, 312
Amorphous polymers, 363, 373
Anand model, 366, 370
Anand/Richeton viscoplastic models, 366
Applied stress, 380
Arrhenius-type temperature dependence, 363
Atomic stresses, 1
Atomic vacancy
concentration gradient, 397
flux equation, 406
Atomic vibrations, 81, 100
Average stress, 13
Average stress norm, matrix
alternative expression, 289
Eigen-strain, 285
ensemble average, 286
ensemble-averaged loading function, 290
Eshelby theory, 285
far-field stress, 285
forth rank identity tensor, 286
fourth-rank tensors, 287
homogeneous matrix, 288
macroscopic stress, 288
particle domain, 285
phase configuration, 286
probability density functions, 286
single ellipsoidal inclusion, 285
single inclusion problem, 286
statistical isotropy and uniformity, 287
straightforward derivations, 287
viscoplastic strain, 290
B
Back stress modulus, 376
Backward Euler scheme, 383
Balanced equation, 217, 219
Bénard cells, 116
Blech Length, 405, 406
Blech Product, 405
Blech’s critical length, 396
Boltzmann constant, 97, 98, 207, 379, 418
Boltzmann’s equation, 98
Boltzmann’s mathematical derivation, 180, 181
Boltzmann-Planck formulation, 191
Bulk modulus, 284
C
Caloric equation of state, 95, 96
Cantilever beam, 90
Cartesian components, 219
Cartesian coordinate system, 13, 18, 21, 44, 77
Cartesian tensor, 46
Cauchy and Almansi tensors, 345
Cauchy deformation tensor, 50, 51
Cauchy stress, 356, 361, 368
Cauchy stress tensor, 18, 60, 67, 240
Cauchy tensor, 347–349
Cauchy’s equilibrium equation, 77, 78
Chen’s analytical micromechanical approach,
279
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8
427
A
ABAQUS model, 387
ABAQUS simulation, 388
Action-reaction law, 10
Activation energy, 366, 379, 380
Activation volume, 380
Almansi tensor, 348, 349
Al thin film strips, 404
Alumina trihydrate (ATH), 278, 279, 312
Amorphous polymers, 363, 373
Anand model, 366, 370
Anand/Richeton viscoplastic models, 366
Applied stress, 380
Arrhenius-type temperature dependence, 363
Atomic stresses, 1
Atomic vacancy
concentration gradient, 397
flux equation, 406
Atomic vibrations, 81, 100
Average stress, 13
Average stress norm, matrix
alternative expression, 289
Eigen-strain, 285
ensemble average, 286
ensemble-averaged loading function, 290
Eshelby theory, 285
far-field stress, 285
forth rank identity tensor, 286
fourth-rank tensors, 287
homogeneous matrix, 288
macroscopic stress, 288
particle domain, 285
phase configuration, 286
probability density functions, 286
single ellipsoidal inclusion, 285
single inclusion problem, 286
statistical isotropy and uniformity, 287
straightforward derivations, 287
viscoplastic strain, 290
B
Back stress modulus, 376
Backward Euler scheme, 383
Balanced equation, 217, 219
Bénard cells, 116
Blech Length, 405, 406
Blech Product, 405
Blech’s critical length, 396
Boltzmann constant, 97, 98, 207, 379, 418
Boltzmann’s equation, 98
Boltzmann’s mathematical derivation, 180, 181
Boltzmann-Planck formulation, 191
Bulk modulus, 284
C
Caloric equation of state, 95, 96
Cantilever beam, 90
Cartesian components, 219
Cartesian coordinate system, 13, 18, 21, 44, 77
Cartesian tensor, 46
Cauchy and Almansi tensors, 345
Cauchy deformation tensor, 50, 51
Cauchy stress, 356, 361, 368
Cauchy stress tensor, 18, 60, 67, 240
Cauchy tensor, 347–349
Cauchy’s equilibrium equation, 77, 78
Chen’s analytical micromechanical approach,
279
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8
427