Classical irreversible thermodynamics, 116
Clausius –Duhem inequality, 80, 91, 93, 94,
101, 103, 107, 110, 224, 226, 351,
420
Coefficient of thermal expansion (CTE), 279,
334
Composite materials, 277
Composite sphere assemblage (CSA), 309, 316
Computational mechanics, 2
Concentration gradient
atomic vacancy, 397
component, 396
driving force, 399
magnitude, 399
Conduction band electrons collide (scatter), 400
Conservation laws, 216
energy, 221–223
entropy (see Entropy law and balance)
fully coupled thermo-mechanical equations,
229
local momentum, 216
mass, 217, 218
momentum principle (see Momentum
principle)
systematic macroscopic scheme, 216
Conservation of energy law, 351
Conservation of mass principle, 63, 64
Conservation of moment of momentum
principle, 68–70
Conservation of momentum principle
Cartesian coordinate system, 67, 68
Cauchy stress tensor, 67
equilibrium of forces, 65
force, 66
Newtonian continuum mechanics, 66
normal stresses, 65
shear stresses, 65
tensile stress, 65
time rate of change, 66, 67
Consistency parameter-Classical theory, 215
Constitutive model approaches, 206
Constitutive model framework, 370
Constitutive relations
dual- and trial-mechanism models, 360
dual-mechanism constitutive models, 360
intermolecular resistance, 361–367
inter-molecular structure, 360
material model, 360
molecular network resistance, 367–371
molecular network structure, 360
Continuous medium
continuity, 2
homogeneity, 2
isotropy, 2
stress, 1
Continuous one-to-one mapping, 343
Continuum mechanics
atomic stresses, 1
continuous functions, 1
continuous medium, 1
definitions, 1
displacement vectors, 57
laws of Newton, 115
molecular structure, 1
Newton’s universal laws of motion
(see Newton’s universal laws of
motion)
shear strain, 59
small strain, 57, 58
St Venant’s compatibility equations, 59, 60
strain, 2
strain-displacement relations, 58
stress, 2
thermodynamics (see Thermodynamics)
Continuum plasticity, 277
Continuum stresses, 1
Contribution
types, 400
Cosserat continuum, 3
Cosserat continuum thermomechanical analysis
couple stress theory (see Cosserat’s couple
stress theory)
equilibrium equations/problem formulation
deformation state, 245
differential element, 245
general solid, 245
general strain gradient plasticity theory,
248
interpretations, 245
kinematic degrees of freedom, 245
rotation and micro rotation, 245
stiffness, 245
surface traction vector, 246
symmetric/anti-symmetric components,
246
theories, 245
function/reduced integration scheme, 237
geometrical factor, 235, 236
gradient plasticity theories, 235
higher order stress theory (see ToupinMindlin higher order stress theory)
mechanics formulation, 234
translational/rotational degrees, 236
Cosserat’s couple stress theory
classical continuum mechanics, 237
elastic constitutive tensors, 241
428
Index
Clausius –Duhem inequality, 80, 91, 93, 94,
101, 103, 107, 110, 224, 226, 351,
420
Coefficient of thermal expansion (CTE), 279,
334
Composite materials, 277
Composite sphere assemblage (CSA), 309, 316
Computational mechanics, 2
Concentration gradient
atomic vacancy, 397
component, 396
driving force, 399
magnitude, 399
Conduction band electrons collide (scatter), 400
Conservation laws, 216
energy, 221–223
entropy (see Entropy law and balance)
fully coupled thermo-mechanical equations,
229
local momentum, 216
mass, 217, 218
momentum principle (see Momentum
principle)
systematic macroscopic scheme, 216
Conservation of energy law, 351
Conservation of mass principle, 63, 64
Conservation of moment of momentum
principle, 68–70
Conservation of momentum principle
Cartesian coordinate system, 67, 68
Cauchy stress tensor, 67
equilibrium of forces, 65
force, 66
Newtonian continuum mechanics, 66
normal stresses, 65
shear stresses, 65
tensile stress, 65
time rate of change, 66, 67
Consistency parameter-Classical theory, 215
Constitutive model approaches, 206
Constitutive model framework, 370
Constitutive relations
dual- and trial-mechanism models, 360
dual-mechanism constitutive models, 360
intermolecular resistance, 361–367
inter-molecular structure, 360
material model, 360
molecular network resistance, 367–371
molecular network structure, 360
Continuous medium
continuity, 2
homogeneity, 2
isotropy, 2
stress, 1
Continuous one-to-one mapping, 343
Continuum mechanics
atomic stresses, 1
continuous functions, 1
continuous medium, 1
definitions, 1
displacement vectors, 57
laws of Newton, 115
molecular structure, 1
Newton’s universal laws of motion
(see Newton’s universal laws of
motion)
shear strain, 59
small strain, 57, 58
St Venant’s compatibility equations, 59, 60
strain, 2
strain-displacement relations, 58
stress, 2
thermodynamics (see Thermodynamics)
Continuum plasticity, 277
Continuum stresses, 1
Contribution
types, 400
Cosserat continuum, 3
Cosserat continuum thermomechanical analysis
couple stress theory (see Cosserat’s couple
stress theory)
equilibrium equations/problem formulation
deformation state, 245
differential element, 245
general solid, 245
general strain gradient plasticity theory,
248
interpretations, 245
kinematic degrees of freedom, 245
rotation and micro rotation, 245
stiffness, 245
surface traction vector, 246
symmetric/anti-symmetric components,
246
theories, 245
function/reduced integration scheme, 237
geometrical factor, 235, 236
gradient plasticity theories, 235
higher order stress theory (see ToupinMindlin higher order stress theory)
mechanics formulation, 234
translational/rotational degrees, 236
Cosserat’s couple stress theory
classical continuum mechanics, 237
elastic constitutive tensors, 241
428
Index