Laws of unified mechanics theory
second law, 133, 134
third law, 134
Legendre-Fenchel transformation, 107
Light emitting diodes (LEDs), 131
Linearization (Consistent Jacobian)
coupling, 213
identity tensors, 212
Newton-Raphson algorithm, 213
thermodynamic state index rate, 212
yield surface, 212
Local coordinates, 26, 32, 33, 36–38
Local equilibrium assumption, 224
Local Newton iteration, 274
M
Macroscopic conservation laws, 215
Macroscopic stress, 288
Mass conservation, 217, 218
Mass transport, 403
Mass/vacancy conservation law, 407–411
Material behavior, 365, 370
Material behavior modeling, 2
Material coordinates, 32–35, 38
Material properties
definition, 373–376
isothermal and non-isothermal conditions,
377
PMMA, 377–379, 381–383
MatLAB, 380
Matrix-filler inter-phase properties
cyclic stress-strain response, 337
finite element simulation, 336, 337
particulate composites, 333, 334, 336
PMMA, 333
Poisson ratio and CTE, 333
Maximum normal stress, 22
Maxwell’s equation, 398, 415
Mechanical damage, 389
Mechanical theory of heat
entropy, 138
equilibrium, 138
formulation, 138
kinetic energy (see Kinetic energy)
thermal equilibrium, 139
Mechanical work dissipation, 109
Mechano-Thermodynamics theory, 129
Memory, 74
Mesh sensitivity, 386, 387
Metal fatigue fracture, 390
Micro-cracks/micro-cavities, 207
Microelectronics, 396, 398
Micromechanical constitutive model,
particulate composite
analytical and numerical models, 316
consistent elastic-viscoplastic tangent
modulus
combining equation, 331
differentiating equation, 329, 330
increment stress-strain relationship, 329
notion, 329
elastic properties, 317–320
imperfect interface, 316
interfacial transition zone, 316
matrix material, 316
matrix-filler inter-phase (see Matrix-filler
inter-phase properties)
modeling process
equivalence, 317, 318
interface properties, 316
micromechanics, 319
simplification, 316
thermomechanical properties, 317, 318
solution algorithm (see General returnmapping algorithm)
TSI, 324
verification examples
ATH material properties, 332
PMMA properties, 332
viscoplasticity (see Viscoplasticity model)
Microstates, 97
Minimum normal stress, 22
Mises rate-independent plasticity, 203
Molecular network mechanism, 352
Molecular network resistance, 367–371, 380
Molecular network structure, 360
Molecular orientation, 367
Molecular relaxation, 369
Molecular structure, 1
Momentum principle, 220
balanced equation, 219
Cartesian coordinates, 219
conservative body forces, 220
deformation tensor rate, 220
displacement gradient components, 220
expression, 218
kinetic energy, 221
long/short-range interactions, 219
Newton’s Third Law, 218
potential energy density, 221
rectangular coordinates, 218
surface integral, 219
time rate, 218
Index
435
second law, 133, 134
third law, 134
Legendre-Fenchel transformation, 107
Light emitting diodes (LEDs), 131
Linearization (Consistent Jacobian)
coupling, 213
identity tensors, 212
Newton-Raphson algorithm, 213
thermodynamic state index rate, 212
yield surface, 212
Local coordinates, 26, 32, 33, 36–38
Local equilibrium assumption, 224
Local Newton iteration, 274
M
Macroscopic conservation laws, 215
Macroscopic stress, 288
Mass conservation, 217, 218
Mass transport, 403
Mass/vacancy conservation law, 407–411
Material behavior, 365, 370
Material behavior modeling, 2
Material coordinates, 32–35, 38
Material properties
definition, 373–376
isothermal and non-isothermal conditions,
377
PMMA, 377–379, 381–383
MatLAB, 380
Matrix-filler inter-phase properties
cyclic stress-strain response, 337
finite element simulation, 336, 337
particulate composites, 333, 334, 336
PMMA, 333
Poisson ratio and CTE, 333
Maximum normal stress, 22
Maxwell’s equation, 398, 415
Mechanical damage, 389
Mechanical theory of heat
entropy, 138
equilibrium, 138
formulation, 138
kinetic energy (see Kinetic energy)
thermal equilibrium, 139
Mechanical work dissipation, 109
Mechano-Thermodynamics theory, 129
Memory, 74
Mesh sensitivity, 386, 387
Metal fatigue fracture, 390
Micro-cracks/micro-cavities, 207
Microelectronics, 396, 398
Micromechanical constitutive model,
particulate composite
analytical and numerical models, 316
consistent elastic-viscoplastic tangent
modulus
combining equation, 331
differentiating equation, 329, 330
increment stress-strain relationship, 329
notion, 329
elastic properties, 317–320
imperfect interface, 316
interfacial transition zone, 316
matrix material, 316
matrix-filler inter-phase (see Matrix-filler
inter-phase properties)
modeling process
equivalence, 317, 318
interface properties, 316
micromechanics, 319
simplification, 316
thermomechanical properties, 317, 318
solution algorithm (see General returnmapping algorithm)
TSI, 324
verification examples
ATH material properties, 332
PMMA properties, 332
viscoplasticity (see Viscoplasticity model)
Microstates, 97
Minimum normal stress, 22
Mises rate-independent plasticity, 203
Molecular network mechanism, 352
Molecular network resistance, 367–371, 380
Molecular network structure, 360
Molecular orientation, 367
Molecular relaxation, 369
Molecular structure, 1
Momentum principle, 220
balanced equation, 219
Cartesian coordinates, 219
conservative body forces, 220
deformation tensor rate, 220
displacement gradient components, 220
expression, 218
kinetic energy, 221
long/short-range interactions, 219
Newton’s Third Law, 218
potential energy density, 221
rectangular coordinates, 218
surface integral, 219
time rate, 218
Index
435