534
Index
Principal stress, 103, 104
Pseudoelasticity, 131
Q
Quick-release test, 221
R
Rate-of-deformation tensor, 92
Reaction stresses, 134
Remodeling
alternative theory, 383–386
arteries (see Arteries growth and
remodeling)
fiber orientation, 387–393
Humphrey-Rajagopal remodeling theory,
346
mechanics, 344–346
Wolff’s law, 341
Remodeling theory
kinematics, 367–369
turnover kinematics
elastic deformation, 350–351
growth, 351–353
Residual stress
artery, 272
brain, 480
opening angle, 371–378
soft tissues, 273–281
Response functions, 134
RHM theory, 401, 407, 434, 480, 486, 489
Rhombomere, 463–465
Rodriguez, Hoger and McCulloch (RHM)
equations, 3D, 283–284
fundamental ideas, 255
growing body configurations, 282
residual stress, 285
volumetric growth, 255–257
zero-stress configuration, 281
ZSS, 255
Rotation tensor, 34, 36, 39
S
Saint-Venant’s principle, 93
Sarcomeres, 210
Sea squirts (ascidians), 404, 438–439
Sea urchin gastrulation, 433, 436–438, 461,
498–499
Second Piola-Kirchhoff stress vector, 96–98,
101, 131
Shape functions, 473, 474
Shear strain, 71–72
Shear stresses
simple shear, 165, 168
Shortening velocity, 220–221
Simple shear, 165, 168, 173
Skeletal muscle, 223, 307, 308
S-looping, 448, 455
Smooth muscle, 219–221, 371
Spatial (Eulerian) coordinate, 41–42, 56
Spherical polar coordinates
deformation gradient, 521
equations of motion, 521
Spherical shell
inflation, 189, 190, 194
limit-point instability, 193, 194
membrane approximation, 192–193, 195
Spinal cord, 10
SPL, see Splanchnopleure (SPL)
Splanchnopleure (SPL), 443–447, 451–455
Stability, 455, 469–471
Stable equilibrium, 469, 471
Strain-displacement relations, 72, 147
Strain-energy density function, 131, 261, 263,
407, 451
Blatz-Ko, 138, 207
experimental considerations, 143
exponential, 138
local action, 135
material symmetry, 135
Mooney-Rivlin, 137
neo-Hookean, 136, 137
objectivity (frame indifference), 135
orthotropy, 142–143
physical admissibility, 135
transverse isotropy, 140–141
Strain invariants, 86
Strain tensor
Lagrangian strain tensor, 77, 79, 81
Strain transformation, 83–84
Stress
body forces, 94
Cauchy’s stress formula, 100
Cauchy stress tensor, 100, 102
Cauchy stress vectors, 100, 101
contact forces, 93
and equilibrium, 198
fiber, 6
first Piola-Kirchhoff stress tensor, 101, 102
1D, 93–94
power, 125–126
principal invariants, 32
second Piola-Kirchhoff stress tensor, 101,
102
3D, 99–103
transformation, 103–104
Index
Principal stress, 103, 104
Pseudoelasticity, 131
Q
Quick-release test, 221
R
Rate-of-deformation tensor, 92
Reaction stresses, 134
Remodeling
alternative theory, 383–386
arteries (see Arteries growth and
remodeling)
fiber orientation, 387–393
Humphrey-Rajagopal remodeling theory,
346
mechanics, 344–346
Wolff’s law, 341
Remodeling theory
kinematics, 367–369
turnover kinematics
elastic deformation, 350–351
growth, 351–353
Residual stress
artery, 272
brain, 480
opening angle, 371–378
soft tissues, 273–281
Response functions, 134
RHM theory, 401, 407, 434, 480, 486, 489
Rhombomere, 463–465
Rodriguez, Hoger and McCulloch (RHM)
equations, 3D, 283–284
fundamental ideas, 255
growing body configurations, 282
residual stress, 285
volumetric growth, 255–257
zero-stress configuration, 281
ZSS, 255
Rotation tensor, 34, 36, 39
S
Saint-Venant’s principle, 93
Sarcomeres, 210
Sea squirts (ascidians), 404, 438–439
Sea urchin gastrulation, 433, 436–438, 461,
498–499
Second Piola-Kirchhoff stress vector, 96–98,
101, 131
Shape functions, 473, 474
Shear strain, 71–72
Shear stresses
simple shear, 165, 168
Shortening velocity, 220–221
Simple shear, 165, 168, 173
Skeletal muscle, 223, 307, 308
S-looping, 448, 455
Smooth muscle, 219–221, 371
Spatial (Eulerian) coordinate, 41–42, 56
Spherical polar coordinates
deformation gradient, 521
equations of motion, 521
Spherical shell
inflation, 189, 190, 194
limit-point instability, 193, 194
membrane approximation, 192–193, 195
Spinal cord, 10
SPL, see Splanchnopleure (SPL)
Splanchnopleure (SPL), 443–447, 451–455
Stability, 455, 469–471
Stable equilibrium, 469, 471
Strain-displacement relations, 72, 147
Strain-energy density function, 131, 261, 263,
407, 451
Blatz-Ko, 138, 207
experimental considerations, 143
exponential, 138
local action, 135
material symmetry, 135
Mooney-Rivlin, 137
neo-Hookean, 136, 137
objectivity (frame indifference), 135
orthotropy, 142–143
physical admissibility, 135
transverse isotropy, 140–141
Strain invariants, 86
Strain tensor
Lagrangian strain tensor, 77, 79, 81
Strain transformation, 83–84
Stress
body forces, 94
Cauchy’s stress formula, 100
Cauchy stress tensor, 100, 102
Cauchy stress vectors, 100, 101
contact forces, 93
and equilibrium, 198
fiber, 6
first Piola-Kirchhoff stress tensor, 101, 102
1D, 93–94
power, 125–126
principal invariants, 32
second Piola-Kirchhoff stress tensor, 101,
102
3D, 99–103
transformation, 103–104