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Ph.D. thesis, Eindhoven University of Technology.
[18] Zienkiewicz, O. C. (1989) The Finite Element Method, 4th edition (McGraw-Hill).
Index


θ -scheme, 267 creep function, 83
cross product, 3
Almansi Euler strain tensor, 179
anisotropy, 314 Darcy™s law, 206
assembly process, 242, 244 deformation
gradient tensor, 172
matrix, 163
basis
tensor, 163, 172
arbitrary, 18
degeneration, 299
Cartesian, 4, 18
differential equation
orthogonal, 4
partial, 264
orthogonal, 18
diffusion coef¬cient, 206
orthonormal, 4, 18
diffusion equation, 232, 278
bending of a beam, 322
divergence theorem, 279
Boltzmann integral, 83
dot product, 2
boundary conditions, 265
dyadic product, 4
essential, 105, 233
natural, 105, 233
boundary value problem, 106 eigenvalue, 147
Bubnov Galerkin, 241 eigenvector, 129, 147
bulk modulus, 196 elastic behaviour, 194
element
bilinear, 297
cantilever beam, 44
isoparametric, 297
Cartesian basis, 116
Lagrangian, 302
Cauchy Green tensor
quadrilateral, 297
left, 175
Serendipity, 302
right, 174
triangular, 299
commutative, 2
element column, 282
completeness, 295
element matrix, 282
compression modulus, 196, 313
element Peclet number, 270
con¬guration
elongational rate, 71
material, 156
equilibrium equations, 139
con¬ned compression, 207
Eulerian description, 158
constitutive model, 50, 194
convection, 160
¬bre, 50
convection-diffusion equation, 264, 283
elastic, 50
convection-diffusion equation 3 D, 277
non-linear, 52
convective
Fick™s law, 206
contribution, 160
Finger tensor, 179
velocity, 160
force
convolution integral, 83
decomposition, 16
coordinates
normal, 16
material, 156
parallel, 16
Couette ¬‚ow, 225
vector, 10, 11
Coulomb friction, 218
force equilibrium, 100, 101
Crank“Nicholson scheme, 267
Fourier number, 266
creep, 83
Index
332

relaxation, 82
free body diagram, 40, 134
relaxation function, 76, 83
friction coef¬cient, 219
relaxation time, 79
retardation time, 82
Galerkin method, 239, 280, 316
Gaussian integration, 249, 305
scalar multiplication, 13
geometrically non-linear, 57, 212
shape functions, 237
Green Lagrange strain tensor, 176
shear modulus, 196
snap through, 59
harmonic excitation, 84
spatial discretization, 269
Heaviside function, 74
spin tensor, 127
homogenization, 114, 119
static equilibrium, 37
Hooke™s law, 195, 314
statically determinate, 40
hydrostatic pressure, 150
statically indeterminate, 40
stent, 288
initial condition, 265
storage modulus, 85
inner product, 2, 14
strain µ, 103
integration by parts, 279
streamline upwind scheme, 273
integration points, 249, 305
stress
integration scheme
deviatoric, 150
Crank“Nicholson, 267
equivalent, 150
backward Euler, 267
hydrostatic, 150
explicit, 267
principal, 146
forward Euler, 267
tensor, 142
implicit, 267
Tresca, 150
internal mechanical energy, 190
vector, 132
isochoric deformation, 180 von Mises, 150
isoparametric, 246, 284, 298 stress σ , 102
isotropy, 195, 314 stretch ratio, 173
superposition, 74
Kelvin“Voigt model, 82
kinetic energy, 189 temporal discretization, 266
tensor
Lagrangian description, 158 de¬nition, 4
deformation rate, 181
line-of-action, 10
determinant, 129
linear elastic stress strain relation, 104
deviatoric, 129
linear elasticity, 313
invariant, 176
linear strain tensor, 178
inverse, 128
local coordinate system, 284
objective, 176
loss Modulus, 85
product, 4
rotation velocity, 181
matrices
spin, 181
pos, 251
trace, 129
top, 250
time derivative
Maxwell model, 78, 79
material, 158
muscle
spatial, 158
contraction, 54
transfer function, 90
myo¬brils, 53
triple product, 3
Trouton™s law, 205
Navier“Stokes equation, 222
Newton™s law, 12
vector addition, 13
Newtonian ¬‚uid, 204
vector basis, 4, 17
non-Newtonian ¬‚uid, 205
vector product, 3
numerical integration, 248, 284, 305
viscosity, 204
viscous behaviour, 71
Peclet number, 266
permeability, 206 weak form, 236, 280, 283
Poiseuille ¬‚ow, 224 weak formulation, 315
polynomial interpolation, 237 weighted residuals, 235
polynomials weighting function, 235
Lagrangian, 302
Young™s modulus, 313
proportionality, 74

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