Multiphase composites, 277
Multi-phase composites elastic moduli, 301
N
Nabarro–Herring model, 405
Natural radiation, 182
Natural sciences, 117
Newton’s universal laws of motion
classical mechanics, 5
conservation laws, 12
first law, 6, 7
range of validity, 11
second law, 8, 9
thermodynamics, 12
third law, 9–11
Newtonian (continuum) mechanics, 94–96
Newtonian mechanic formulation, 281
Newtonian mechanics, 73, 80, 94, 100, 106,
107, 124, 336
force equilibrium, 411, 412
Newton-Raphson integration algorithm, 274
Nodal values, 408
Non-associative plasticity, 109
Non-conservative forces, 371
Non-dimensional interface parameter, 313
Non-equilibrium states, 84
Non-interacting solution
average stress norm (see Average stress
norm, matrix)
elastoplastic response, 284
isotropic hardening function, 284
particles average stress, 290, 291
statistical/microstructural information, 284
yield function, 284
Non-isothermal conditions, 360
Non-isothermal loading, 365
Non-isothermal simulations, 380
Non-isothermal stretching
PMMA, 390–391
Non-isothermal tests, 376
Nonlinearities, 205
Non-linear-kinematic hardening (NLK) rule,
205, 206
Non-negative consistency parameter, 206
Non-steady state diffusion, 399, 400
Normal stresses, 65
O
Observable thermodynamics variables, 100
Ohm's law, 412
Onsager reciprocal relations, 109–112
Ordered state, 96
P
Pairwise interacting solution
approximate solutions (see Two-phase
interaction approximate solutions)
ensemble-average stress norm, filler
particles, 298
ensemble-average stress norm, matrix, 295
Particle filled composites, 279
Particle-matrix interactions and microstructure,
282
Particulate composites
analytical predictions, 278
constituent phases, 277
interfacial layer, 309
matrix and particles, 280
microstructure, 279
plastic strain, 286
relationships, 278
shear modulus, 311
Permutability measure, 136, 137, 174–176
Phenomenological curve fitting methods, 115
Phenomenological equations, 111
Phonons, 81, 93
Piola-Kirchhoff stress tensor, 103, 358, 361,
362
Cauchy stress tensor, 60
Lagrangian stress tensor, 60, 61
material formulation, 60
referential coordinate system, 60
second Piola-Kirchhoff, 61, 62
Planck, 136
Plastic deformation, 194
Plastic deformation gradient, 344, 349, 363,
369
Plastic flow, 364
Plastic flow behavior, 367
Plastic flow resistance, 364
molecular network, 375
Plastic strain rate, 364
Plastic stretch, 350, 357, 362, 369, 370
Plastic stretch rate tensors, 384
Plasticity, 106, 107
theory, 380
Ply-methyl-meth-acrylate (PMMA)
glass transition temperature, 377
isothermal and non-isothermal stretching,
376
isothermal stretching, 384–390
isothermal tests, 377
material parameters, 383
material properties, 377
non-isothermal stretching, 390–392
rate dependent glass transition temperature,
377
436
Index
Multi-phase composites elastic moduli, 301
N
Nabarro–Herring model, 405
Natural radiation, 182
Natural sciences, 117
Newton’s universal laws of motion
classical mechanics, 5
conservation laws, 12
first law, 6, 7
range of validity, 11
second law, 8, 9
thermodynamics, 12
third law, 9–11
Newtonian (continuum) mechanics, 94–96
Newtonian mechanic formulation, 281
Newtonian mechanics, 73, 80, 94, 100, 106,
107, 124, 336
force equilibrium, 411, 412
Newton-Raphson integration algorithm, 274
Nodal values, 408
Non-associative plasticity, 109
Non-conservative forces, 371
Non-dimensional interface parameter, 313
Non-equilibrium states, 84
Non-interacting solution
average stress norm (see Average stress
norm, matrix)
elastoplastic response, 284
isotropic hardening function, 284
particles average stress, 290, 291
statistical/microstructural information, 284
yield function, 284
Non-isothermal conditions, 360
Non-isothermal loading, 365
Non-isothermal simulations, 380
Non-isothermal stretching
PMMA, 390–391
Non-isothermal tests, 376
Nonlinearities, 205
Non-linear-kinematic hardening (NLK) rule,
205, 206
Non-negative consistency parameter, 206
Non-steady state diffusion, 399, 400
Normal stresses, 65
O
Observable thermodynamics variables, 100
Ohm's law, 412
Onsager reciprocal relations, 109–112
Ordered state, 96
P
Pairwise interacting solution
approximate solutions (see Two-phase
interaction approximate solutions)
ensemble-average stress norm, filler
particles, 298
ensemble-average stress norm, matrix, 295
Particle filled composites, 279
Particle-matrix interactions and microstructure,
282
Particulate composites
analytical predictions, 278
constituent phases, 277
interfacial layer, 309
matrix and particles, 280
microstructure, 279
plastic strain, 286
relationships, 278
shear modulus, 311
Permutability measure, 136, 137, 174–176
Phenomenological curve fitting methods, 115
Phenomenological equations, 111
Phonons, 81, 93
Piola-Kirchhoff stress tensor, 103, 358, 361,
362
Cauchy stress tensor, 60
Lagrangian stress tensor, 60, 61
material formulation, 60
referential coordinate system, 60
second Piola-Kirchhoff, 61, 62
Planck, 136
Plastic deformation, 194
Plastic deformation gradient, 344, 349, 363,
369
Plastic flow, 364
Plastic flow behavior, 367
Plastic flow resistance, 364
molecular network, 375
Plastic strain rate, 364
Plastic stretch, 350, 357, 362, 369, 370
Plastic stretch rate tensors, 384
Plasticity, 106, 107
theory, 380
Ply-methyl-meth-acrylate (PMMA)
glass transition temperature, 377
isothermal and non-isothermal stretching,
376
isothermal stretching, 384–390
isothermal tests, 377
material parameters, 383
material properties, 377
non-isothermal stretching, 390–392
rate dependent glass transition temperature,
377
436
Index