ratio of yield stress to temperature vs. plastic
strain rate plot, 379
reference glass transition temperature, 365
storage modulus and elastic modulus, 374
stress-strain curves, 382
temperature and rate dependent elastic
modulus, 377, 378
temperature and rate dependent limited
chain extensibility, 378
temperature dependent back stress modulus,
381
thermal properties, 377
Poisson’s ratio, 278, 281, 312, 313, 333, 374,
378
Polyatomic gas molecules
external forces, 161
generalized coordinates, 161
gravity, 163
integration, 165
molecules, 162, 164
state distributions, 163
Polymer, 343
Poly-methyl methacrylate (PMMA), 278–280
Polynomial theorem, 173
Potential
thermodynamic (see Thermodynamic
potential)
Potential function, 76, 101, 109
Power-exponent free product, 165
complexions, 171
kinetic energy, 167–169, 171
mono-atomic gases, 165
polynomial coefficient, 173
polynomial theorem, 173
probability determination, 172
quantity, 165
Regula falsi, 166
state distribution, 171–174
values, 167
velocity components, 169
Prager-Ziegler rule, 258
Prigogine’s dissipative structure theory, 117
Prigogine’s thermodynamics, 116
Probability density functions, 286
Probability distribution
permutability measure, 174, 176–178
potential energy, 179
reversible change of state, 175
second law of thermodynamics, 179
theory of gases, 180
thermal equilibrium, 174, 176
velocity components, 174
Prolonged ductile failure, 373
Pseudo potential, 106
Pseudo-static loading, 105
Pseudo-thermodynamics forces, 120
Pure rigid body motion, 31
Q
Quantum mechanics, 10, 13
Quasi-static electro-chemical work, 87, 88
Quasi-static processes, 111
Quasi-static work, 86
R
Rate of deformation tensor
definition, 43
small strain tensor, 44, 45
spin matrix, 44
stretching tensor, 43
true strain, 45, 46
Rayleigh-Bénard instability, 116
Reaction force, 11
Recoverable work, 103
Reduced Cosserat, 242
Reduced couple stress theory
asymmetric component, 252
displacement functions, 251
finite element method implementation, 252
virtual displacements, 251
virtual work, 252
Reference coordinate system, 343
Reference frame
Almansi tensor, 348
Cauchy tensor, 347, 348
elastic and plastic velocity gradient, 350
elastic stretch rate tensor, 350
plastic deformation gradient, 349
quantity/equation, 347
rotation tensor, 347
spin tensor, 348, 350
stress tensor, 347
stretch rate tensor, 348, 349
transformation rules, 347
velocity gradient, 348
Reference temperature, 379
Referential coordinate system, 42, 63
Regression analysis method, 380
Regula falsi, 166
Relaxation process, 367
Relaxation time, 323, 335
Renormalization procedure, 282
Representative volume element (RVE), 2, 207,
224, 277, 280
Index
437
strain rate plot, 379
reference glass transition temperature, 365
storage modulus and elastic modulus, 374
stress-strain curves, 382
temperature and rate dependent elastic
modulus, 377, 378
temperature and rate dependent limited
chain extensibility, 378
temperature dependent back stress modulus,
381
thermal properties, 377
Poisson’s ratio, 278, 281, 312, 313, 333, 374,
378
Polyatomic gas molecules
external forces, 161
generalized coordinates, 161
gravity, 163
integration, 165
molecules, 162, 164
state distributions, 163
Polymer, 343
Poly-methyl methacrylate (PMMA), 278–280
Polynomial theorem, 173
Potential
thermodynamic (see Thermodynamic
potential)
Potential function, 76, 101, 109
Power-exponent free product, 165
complexions, 171
kinetic energy, 167–169, 171
mono-atomic gases, 165
polynomial coefficient, 173
polynomial theorem, 173
probability determination, 172
quantity, 165
Regula falsi, 166
state distribution, 171–174
values, 167
velocity components, 169
Prager-Ziegler rule, 258
Prigogine’s dissipative structure theory, 117
Prigogine’s thermodynamics, 116
Probability density functions, 286
Probability distribution
permutability measure, 174, 176–178
potential energy, 179
reversible change of state, 175
second law of thermodynamics, 179
theory of gases, 180
thermal equilibrium, 174, 176
velocity components, 174
Prolonged ductile failure, 373
Pseudo potential, 106
Pseudo-static loading, 105
Pseudo-thermodynamics forces, 120
Pure rigid body motion, 31
Q
Quantum mechanics, 10, 13
Quasi-static electro-chemical work, 87, 88
Quasi-static processes, 111
Quasi-static work, 86
R
Rate of deformation tensor
definition, 43
small strain tensor, 44, 45
spin matrix, 44
stretching tensor, 43
true strain, 45, 46
Rayleigh-Bénard instability, 116
Reaction force, 11
Recoverable work, 103
Reduced Cosserat, 242
Reduced couple stress theory
asymmetric component, 252
displacement functions, 251
finite element method implementation, 252
virtual displacements, 251
virtual work, 252
Reference coordinate system, 343
Reference frame
Almansi tensor, 348
Cauchy tensor, 347, 348
elastic and plastic velocity gradient, 350
elastic stretch rate tensor, 350
plastic deformation gradient, 349
quantity/equation, 347
rotation tensor, 347
spin tensor, 348, 350
stress tensor, 347
stretch rate tensor, 348, 349
transformation rules, 347
velocity gradient, 348
Reference temperature, 379
Referential coordinate system, 42, 63
Regression analysis method, 380
Regula falsi, 166
Relaxation process, 367
Relaxation time, 323, 335
Renormalization procedure, 282
Representative volume element (RVE), 2, 207,
224, 277, 280
Index
437