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 |  موضوع: كتاب Finite Element Analysis for Biomedical Engineering Applications الأربعاء 14 أغسطس 2024 - 1:37 | |
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أخواني في الله
أحضرت لكم كتاب
Finite Element Analysis for Biomedical Engineering Applications
Z. Yang
و المحتوى كما يلي :
Contents
Preface . xiii
About the Author . xv
Chapter 1 Introduction . 1
PART I Bone
Chapter 2 Bone Structure and Material Properties . 5
2.1 Bone Structure . 5
2.2 Material Properties of Bone . 7
References 8
Chapter 3 Simulation of Nonhomogeneous Bone 9
3.1 Building Bone Model from CT Data . 9
3.1.1 CT Data 10
3.1.2 Finite Element Model . 10
3.1.3 Calculation of the Average CT Number (HU) 10
3.1.4 Material Property Assignment . 13
3.1.5 Discussion 14
3.1.6 Summary . 14
3.2 Interpolation of Bone Material Properties . 15
3.2.1 Multidimensional Interpolation 15
3.2.1.1 RBAS Algorithm . 15
3.2.1.2 NNEI Algorithm 15
3.2.1.3 LMUL Algorithm . 16
3.2.2 Interpolation of Material Properties of
the Ankle . 16
3.2.2.1 Defining Material Properties of
Bone Using the RBAS Algorithm 18
3.2.2.2 Defining Material Properties of
Bone Using the NNEI Algorithm 18
3.2.2.3 Defining Material Properties of
Bone Using the LMUL Algorithm . 18
3.2.2.4 Defining Material Properties of
Bone Using a Mixed Method 19
3.2.3 Discussion 20
3.2.4 Summary . 21
References . 21
vChapter 4 Simulation of Anisotropic Bone . 23
4.1 Anisotropic Material Models . 23
4.2 Finite Element Model of Femur with Anisotropic
Materials 25
4.2.1 Finite Element Model of Femur with
Anisotropic Materials . 25
4.2.2 Simulation of Mechanical Testing of the Femur 29
4.2.3 Discussion 29
4.2.4 Summary . 31
References . 31
Chapter 5 Simulation of Crack Growth Using the eXtended Finite
Element Method (XFEM) . 33
5.1 Introduction to XFEM . 33
5.1.1 Singularity-Based Method . 33
5.1.2 Phantom-Node Method 34
5.1.3 General Process for Performing XFEM
Crack-Growth Simulation . 35
5.2 Simulation of Crack Growth of the Cortical Bone . 35
5.2.1 Finite Element Model . 37
5.2.1.1 Geometry and Mesh . 37
5.2.1.2 Material Properties 37
5.2.1.3 Definition of Crack Front 38
5.2.1.4 Local Coordinate Systems . 38
5.2.1.5 Loading and Boundary Conditions . 39
5.2.1.6 Solution Setting . 39
5.2.2 Results . 40
5.2.3 Discussion 41
5.2.4 Summary . 41
References . 42
PART II Soft Tissues
Chapter 6 Structure and Material Properties of Soft Tissues . 45
6.1 Cartilage 45
6.1.1 Structure of Cartilage . 45
6.1.2 Material Properties of Cartilage 45
6.2 Ligaments . 46
6.2.1 Structure of Ligaments 46
6.2.2 Material Properties of Ligaments 46
6.3 Intervertebral Disc . 47
References . 48
vi ContentsChapter 7 Nonlinear Behavior of Soft Tissues 49
7.1 Hyperelastic Models . 49
7.2 Finite Element Analysis of the Abdominal Aortic
Aneurysm Wall 51
7.2.1 Finite Element Model . 52
7.2.1.1 Geometry and Mesh . 52
7.2.1.2 Material Model . 53
7.2.1.3 Loading and Boundary Conditions . 55
7.2.1.4 Solution Setting . 56
7.2.2 Results . 56
7.2.3 Discussion 57
7.2.4 Summary . 58
References . 58
Chapter 8 Viscoelasticity of Soft Tissues 61
8.1 The Maxwell Model . 61
8.2 Study of PDL Creep . 63
8.2.1 Finite Element Model . 63
8.2.1.1 Geometry and Mesh . 63
8.2.1.2 Material Models 64
8.2.1.3 Boundary Conditions 64
8.2.1.4 Loading Steps . 65
8.2.2 Results . 65
8.2.3 Discussion 65
8.2.4 Summary . 67
References . 67
Chapter 9 Fiber Enhancement . 69
9.1 Standard Fiber Enhancement . 69
9.1.1 Introduction of Standard Fiber
Enhancement . 69
9.1.2 IVD Model with Fiber Enhancement . 69
9.1.2.1 Finite Element Model of IVD 70
9.1.2.2 Results . 73
9.1.2.3 Discussion 73
9.1.2.4 Summary . 75
9.2 Mesh-Independent Fiber Enhancement 75
9.2.1 Introduction of Mesh-Independent Fiber
Enhancement . 75
9.2.2 IVD Model with Mesh-Independent Fiber
Enhancement . 76
9.2.2.1 Finite Element Model . 76
Contents vii9.2.2.2 Creating the Fibers . 76
9.2.2.3 Results 78
9.2.2.4 Summary 79
9.3 Material Models Including Fiber Enhancement . 79
9.3.1 Anisotropic Material Model with Fiber
Enhancement 79
9.3.2 Simulation of Anterior Cruciate
Ligament (ACL) . 84
9.3.2.1 Finite Element Model 85
9.3.2.2 Results 88
9.3.2.3 Discussion . 88
9.3.2.4 Summary 88
References 90
Chapter 10 USERMAT for Simulation of Soft Tissues . 93
10.1 Introduction of Subroutine UserHyper 93
10.2 Simulation of AAA Using UserHyper 93
10.2.1 Using Subroutine UserHyper to Simulate
Soft Tissues of the Artery 93
10.2.2 Validation . 95
10.2.3 Study the AAA Using UserHyper 96
10.2.4 Discussion 96
10.2.5 Summary 98
References 99
Chapter 11 Modeling Soft Tissues as Porous Media 101
11.1 CPT Elements . 101
11.2 Study of Head Impact 102
11.2.1 Finite Element Model of the Head . 102
11.2.1.1 Geometry and Mesh 102
11.2.1.2 Material Properties 102
11.2.1.3 Loading and Boundary
Conditions 102
11.2.2 Results . 105
11.2.3 Discussion . 108
11.2.4 Summary . 108
11.3 Simulation of Creep Behavior of the IVD . 108
11.3.1 Finite Element Method 108
11.3.1.1 Geometry and Mesh 108
11.3.1.2 Material Properties 108
11.3.1.3 Loading and Boundary
Conditions 109
11.3.1.4 Solution Setting . 109
viii Contents11.3.2 Results . 110
11.3.3 Discussion . 111
11.3.4 Summary . 113
References 113
PART III Joints
Chapter 12 Structure and Function of Joints 117
Reference . 118
Chapter 13 Modeling Contact . 119
13.1 Contact Models . 119
13.2 3D Knee Contact Model . 120
13.2.1 Finite Element Model . 120
13.2.1.1 Geometry and Mesh 120
13.2.1.2 Material Properties 123
13.2.1.3 Contact Pairs . 123
13.2.1.4 Boundary Conditions 127
13.2.2 Results . 128
13.2.3 Discussion . 129
13.2.4 Summary . 130
13.3 2D Poroelastic Model of Knee . 130
13.3.1 Finite Element Model . 131
13.3.1.1 Geometry and Mesh 131
13.3.1.2 Material Properties 133
13.3.1.3 Contact Definitions . 134
13.3.1.4 Boundary Conditions and
Loading 134
13.3.1.5 Solution Setting . 136
13.3.2 Results . 136
13.3.3 Discussion . 137
13.3.4 Summary . 138
References 140
Chapter 14 Application of the Discrete Element Method for Study
of the Knee Joint 141
14.1 Introduction of Discrete Element Method . 141
14.2 Finite Element Model 141
14.2.1 Line-Plane Intersection 142
14.2.2 Building Springs 143
14.2.3 Boundary Conditions . 145
Contents ix14.2.4 Results . 145
14.2.5 Discussion . 146
14.2.6 Summary . 147
References 147
PART IV Simulation of Implants
Chapter 15 Study of Contact in Ankle Replacement 151
15.1 Finite Element Model 151
15.1.1 Geometry and Mesh 151
15.1.2 Material Properties 151
15.1.3 Contact Definition 153
15.1.4 Loading and Boundary Conditions . 153
15.2 Results 154
15.3 Discussion 155
15.4 Summary . 156
References 156
Chapter 16 Simulation of Shape Memory Alloy (SMA)
Cardiovascular Stent 157
16.1 SMA Models 157
16.1.1 SMA Model for Superelasticity 157
16.1.2 SMA Model with Shape Memory Effort . 160
16.2 Simulation of Angioplasty with Vascular Stenting . 161
16.2.1 Finite Element Model . 162
16.2.1.1 Geometry and Mesh 162
16.2.1.2 Material Properties 163
16.2.1.3 Contact Pairs . 164
16.2.1.4 Solution Setting . 165
16.2.2 Results . 166
16.2.3 Discussion . 166
16.2.4 Summary . 167
References 167
Chapter 17 Wear Model of Liner in Hip Replacement 169
17.1 Wear Simulation 169
17.1.1 Archard Wear Model . 169
17.1.2 Improving Mesh Quality during Wear . 169
17.2 Simulating Wear of Liner in Hip Replacement 170
17.2.1 Finite Element Method 170
17.2.1.1 Geometry and Mesh 170
x Contents17.2.1.2 Material Properties 170
17.2.1.3 Wear Model 171
17.2.1.4 Contact Definition 172
17.2.1.5 Loading and Boundary
Conditions 172
17.2.1.6 Solution Setting . 172
17.2.2 Results . 173
17.2.3 Discussion . 173
17.2.4 Summary . 175
References 175
Chapter 18 Fatigue Analysis of a Mini Dental Implant (MDI) . 177
18.1 SMART Crack-Growth Technology 177
18.2 Study of Fatigue Life of an MDI . 178
18.2.1 Finite Element Model . 179
18.2.1.1 Geometry and Mesh 179
18.2.1.2 Material Properties 179
18.2.1.3 Loading and Boundary
Conditions 180
18.2.1.4 Setting up Fracture
Calculation . 180
18.2.2 Results . 181
18.2.3 Discussion . 183
18.2.4 Summary . 184
References 184
PART V Retrospective
Chapter 19 Retrospective . 187
19.1 Principles for Modeling Biology . 187
19.2 Meshing Sensitivity 188
19.3 Units 188
19.4 Workbench 188
19.5 ANSYS Versions 188
Appendix 1: Input File of the Multidimensional Interpolation
in Section 3.2.2 . 189
Appendix 2: Input File of the Anisotropic Femur Model in Section 4.2 203
Appendix 3: Input File of the XFEM Crack-Growth Model in
Section 5.2 . 207
Contents xiAppendix 4: Input File of the Abdominal Aortic Aneurysm Model
in Section 7.2 213
Appendix 5: Input File of the Periodontal Ligament Creep Model
in Section 8.2 217
Appendix 6: Input File of the Intervertebral Disc Model with Fiber
Enhancement in Section 9.1.2 . 221
Appendix 7: Input File of the Intervertebral Disc Model with Mesh
Independent Fiber Enhancement in Section 9.2.2 . 229
Appendix 8: Input File of the Anterior Cruciate Ligament Model
in Section 9.3.2 . 235
Appendix 9: Input File of Subroutine UserHyper in Section 10.2 239
Appendix 10: Input File of the Head Impact Model in Section 11.2 243
Appendix 11: Input File of the Intervertebral Disc Model in Section 11.3 245
Appendix 12: Input File of the Knee Contact Model in Section 13.2 . 249
Appendix 13: Input File of the 2D Axisymmetrical Poroelastic Knee
Model in Section 13.3 . 259
Appendix 14: Input File of the Discrete Element Model of Knee Joint
in Chapter 14 . 265
Appendix 15: Input File of the Material Definition of the Cancellous Bone
in Chapter 15 . 273
Appendix 16: Input File of the Stent Implantation Model in Chapter 16 281
Appendix 17: Input File of the Wear Model of Hip Replacement
in Chapter 17 . 289
Appendix 18: Input File of the Mini Dental Implant Crack-Growth Model
in Chapter 18 293
Index 299
xii Contents
Index
A
abdominal aortic aneurysm (AAA), 1, 43, 49,
51–58, 93–98
ACL, 84–89
anisotropic, 1–3, 8, 14, 23–31, 46, 57, 79–84,
86, 130, 137, 187
anisotropic bone, 1, 3, 23–31
ankle, 1–2, 15–20, 141, 149
ANSYS, 1–2, 10, 15, 23–25, 41, 43, 50, 52–53,
55, 57, 63, 86, 93, 96, 98, 101, 108,
115, 120, 130, 134, 144–145, 159,
161, 167, 169, 188
ANSYS190, 2 ,10, 14–15, 18, 21, 69–70, 75,
82, 88, 149, 151, 169–170, 175, 177,
183, 188
APDL, 2, 12, 53, 55, 82, 98, 109, 145, 188
apparent density, 9, 13
axisymmetrical, 2, 115, 130, 133, 138
B
bone
bone density, 9, 13
cancellous bone, 5, 8, 15–17, 20–21, 28–29,
63–64, 151, 153–156
cortical bone, 1, 3, 5, 7–8, 28, 33, 35–41, 64,
117–118, 151, 184, 187
marrow, 5, 8
periosteum, 5
Wolff’s law, 9, 21
C
cadaver femur, 25–26, 29
Cardiovascular diseases, 161
cartilages, 45, 119–120, 125, 128–134, 137,
141, 146, 187
cement, 37
cohesive, 38
collagen, 5, 45–47
Collagen fibers, 5, 46–47, 69–70, 118
compliance, 23–24
composite material, 5
compression only, 145
contact
always bonded, 119, 125, 129, 187–188
contact pressures, 128–129, 137, 141,
145, 175
MPC, 55, 87, 119, 122, 126, 130, 165,
172, 188
pilot node, 55, 86, 119, 126, 172, 187–188
standard contact, 119, 124, 129–130, 134,
147, 156, 164, 172, 187
coordinate, 27, 86, 146
coordinate systems
element coordinate systems, 86
ESYSs, 29
global coordinate system, 38
local coordinate system, 38–39, 86, 146,
172, 180
nodal coordinates, 144, 146
CSF, 102, 104–106
CT, 1, 9–10, 12–14, 67, 76, 103
CT data, 9–14
curve-fitting, 53–54, 58
CVD, 161
D
discrete element analysis (DEA), 141, 145, 147
Discrete Element Methods, 2, 115, 141–147
degrees of freedom (DOF), 29 ,34, 57, 64, 73,
86, 109, 127, 145, 154, 172, 180
Drucker-Prager function, 157
E
elastic modulus, 49, 61
F
fatigue, 1, 149, 177–184
Paris’ s Law, 179
femoral head, 170, 172, 175
femoral neck, 25
femur, 5–6, 10, 12–14, 25, 29–31, 85, 120,
127, 129, 132, 141, 143, 145, 188
fiber enhancement
Discrete modeling, 69–70
fiber directions, 73, 88
mesh dependent fiber enhancement, 2
mesh independent fiber enhancement, 2, 69,
75–79, 188
299fiber enhancement (Continued)
mesh independent method, 75, 78–79
Smeared modeling, 70, 103
finite element analysis, 1, 51–58, 120, 130,
141, 149
finite element method, 52, 102, 108–110, 120,
170–173
flexibility, 5, 24
force-distributed boundary constraints, 55,
57, 164
fracture, 9, 35, 39
crack front, 33, 35, 38, 41, 177, 181,
183–184
crack-growth, 1, 33, 35, 37
fracture parameter calculation, 39, 177, 180
inclined crack, 37, 39–40
microcracks, 36, 179
path-independent, 183
stress intensity factor, 40, 180–181, 183
H
Haversian channel, 37
Haversian system, 29
head impact, 2, 43, 102–107
HI, 102
history-dependent, 46–47
homogeneous, 8, 102, 187
HU, 10, 12–13
hyperelasticity
hyperelastic materials, 49, 51
hyperelastic models, 49–51
Mooney-Rivlin, 50–51, 95–96, 98, 164, 166
Neo-Hookean, 51, 83
Ogden, 51, 53, 57
I
ICEM, 10
impact, 2, 43, 102–108
implants
ankle arthroplasty, 151
anklereplacement, 1, 2, 151–156, 187
hip implant, 1, 2, 149, 170, 172
hip replacement, 3, 9, 169–175
MDI, 149, 177–183
stent implantation, 1, 2, 149, 161–162,
166
initial strain, 144
inorganic materials, 5
internal friction, 45, 101, 108, 187
interstitial lamellae, 37
isotropic, 8, 14, 25, 27–28, 57, 64, 85, 88, 102,
123, 151, 164, 187
intervertebral discs (IVDs), 1, 2, 43, 45, 47–48,
69–80, 108–113, 187
annulus, 2, 43, 47, 69–76, 108–110, 112
end plate, 47, 70, 73, 108, 118
nucleus, 43, 47, 74, 80, 108–110
K
knee
femoral cartilage, 119, 124–125, 128, 131,
134, 188
meniscus, 119–120, 123–124, 127–134,
137–138, 141, 145, 187
model, 2, 85, 115, 120, 123, 130, 134,
136–139
tibial articular cartilage, 124–125, 131, 134
L
lattice structure, 8, 25
ligaments, 43, 45–47, 119–120
line-plane intersection, 141–143, 146
liner, 1, 170–175
M
material identity, 13, 28, 76
material properties, 1, 5–9, 13–21, 23, 28,
37–38, 45–47, 64, 70–71, 95,
101–102, 104, 108–109, 123,
133, 151–153, 163–164, 170–171,
179, 187
medial tilting, 1–2, 155
meshing
Mesh nonlinear adaptivity, 169
MESH200, 35, 38, 41, 75–76, 184
meshing sensitivity, 188
morph, 172
morphing, 33
regular meshing, 41, 169, 184
remeshing, 33, 169, 177–178, 181
microstructure, 1, 33, 36
MIMICS, 10
multidimensional interpolation, 9, 15
bounding box, 16–21
Linear Multivariate, 15, 151
LMUL, 15–21, 151
Nearest Neighbor, 15
NNEI, 15–16, 18–20, 151
query points, 15–17
300 IndexRadial Basis, 15
RBAS, 15–21, 151, 153
supporting point, 15–16
N
Newton-Raphson method, 110, 136
noises, 14
nonhomogeneity, 14
nonhomogeneous, 1, 8, 9–21, 151, 187
O
organic matrix, 5
orientation, 25, 46, 69–70, 72, 78
orthotropic, 24, 133
Osteoarthritis, 120–121
osteons, 37, 40–41
Osteoporosis, 35–36
P
periodontal ligament (PDL), 1, 43, 61, 63–66
plane strain, 37, 102
plaque, 163–167
plastic strain, 154–156, 166–167
poroelasticity
Biot coefficient, 101
Biot effective stress, 101
Biot’s consolidation theory, 101
biphasic, 101, 108, 111–112, 130
CPT, 101–102, 110, 130, 136, 187
Darcy’s Law, 101
permeability, 101, 102, 108, 109, 187, 188
pore pressure, 101–102, 105–107, 109–112,
113, 134, 136, 137
porosity, 5, 8
porous media, 2, 101–113, 130, 133,
137, 187
Prager-Lode type, 160
principal directions, 27
principal stresses, 25, 27, 29
prosthesis, 9, 161, 178
R
rigid body motion, 55, 105
S
shape functions, 33
skull, 102, 104–105, 117
shape memory alloy (SMA), 149, 157–167
austenite, 160
martensite, 158, 160
phase transformation, 157, 159–160, 167
shape memory effect, 157–158, 161,
163, 167
superelastic effect, 157
superelasticity, 157–159, 163, 167
SMART, 2, 149, 177–178, 180, 183–184, 188
soft tissues, 1–2, 9, 45–48, 49–57, 61–67, 69,
73, 93–98, 101–113, 130, 136,
137–138, 187–188
SpaceClaim, 52, 179
springs, 141, 143–146
stiffness, 8, 23, 157, 187
strain energy potential, 85, 88, 93
swelling, 56, 70, 73
T
talar component, 2, 18, 149, 151–156, 187
Taylor series, 95
tendon, 8, 120
tension only, 71–73, 84
tetrahedral elements, 151
Thermal expansion coefficient, 70
tibia, 85–87, 120, 125–132, 134, 141,
143–144
time-dependent, 46–47, 61
U
USERMAT, 2, 93–98
V
viscoelasticity, 1, 61, 65, 88, 108
creep, 1–2, 61, 63, 65, 108, 111
Maxwell model, 61–63
Prony series, 61–65
von Mises strain, 88–89
von Mises stresses, 29–30, 40–41, 56–57, 66,
74, 78, 80, 88–89, 98, 127, 128–129,
138, 145, 154–155, 166–167
W
wear, 1–2, 149, 169–170, 171, 172–175, 188,
205, 211
Archard Wear Model, 2, 149, 169, 171
coefficient of friction, 45, 117, 156
wear coefficient, 169, 171–172
Index 301X
XFEM, 1, 33–36, 38, 41, 177, 184, 188
enrichment, 33, 40
Phantom-node method, 33–35, 38
Singularity-based method, 33–34
Y
yield stress, 153, 155–156
Young’s modulus, 5, 7, 13, 16–28, 64,
70, 71, 102, 109, 137, 151,
155–15fiber enhancement (Continued)
mesh independent method, 75, 78–79
Smeared modeling, 70, 103
finite element analysis, 1, 51–58, 120, 130,
141, 149
finite element method, 52, 102, 108–110, 120,
170–173
flexibility, 5, 24
force-distributed boundary constraints, 55,
57, 164
fracture, 9, 35, 39
crack front, 33, 35, 38, 41, 177, 181,
183–184
crack-growth, 1, 33, 35, 37
fracture parameter calculation, 39, 177, 180
inclined crack, 37, 39–40
microcracks, 36, 179
path-independent, 183
stress intensity factor, 40, 180–181, 183
H
Haversian channel, 37
Haversian system, 29
head impact, 2, 43, 102–107
HI, 102
history-dependent, 46–47
homogeneous, 8, 102, 187
HU, 10, 12–13
hyperelasticity
hyperelastic materials, 49, 51
hyperelastic models, 49–51
Mooney-Rivlin, 50–51, 95–96, 98, 164, 166
Neo-Hookean, 51, 83
Ogden, 51, 53, 57
I
ICEM, 10
impact, 2, 43, 102–108
implants
ankle arthroplasty, 151
anklereplacement, 1, 2, 151–156, 187
hip implant, 1, 2, 149, 170, 172
hip replacement, 3, 9, 169–175
MDI, 149, 177–183
stent implantation, 1, 2, 149, 161–162,
166
initial strain, 144
inorganic materials, 5
internal friction, 45, 101, 108, 187
interstitial lamellae, 37
isotropic, 8, 14, 25, 27–28, 57, 64, 85, 88, 102,
123, 151, 164, 187
intervertebral discs (IVDs), 1, 2, 43, 45, 47–48,
69–80, 108–113, 187
annulus, 2, 43, 47, 69–76, 108–110, 112
end plate, 47, 70, 73, 108, 118
nucleus, 43, 47, 74, 80, 108–110
K
knee
femoral cartilage, 119, 124–125, 128, 131,
134, 188
meniscus, 119–120, 123–124, 127–134,
137–138, 141, 145, 187
model, 2, 85, 115, 120, 123, 130, 134,
136–139
tibial articular cartilage, 124–125, 131, 134
L
lattice structure, 8, 25
ligaments, 43, 45–47, 119–120
line-plane intersection, 141–143, 146
liner, 1, 170–175
M
material identity, 13, 28, 76
material properties, 1, 5–9, 13–21, 23, 28,
37–38, 45–47, 64, 70–71, 95,
101–102, 104, 108–109, 123,
133, 151–153, 163–164, 170–171,
179, 187
medial tilting, 1–2, 155
meshing
Mesh nonlinear adaptivity, 169
MESH200, 35, 38, 41, 75–76, 184
meshing sensitivity, 188
morph, 172
morphing, 33
regular meshing, 41, 169, 184
remeshing, 33, 169, 177–178, 181
microstructure, 1, 33, 36
MIMICS, 10
multidimensional interpolation, 9, 15
bounding box, 16–21
Linear Multivariate, 15, 151
LMUL, 15–21, 151
Nearest Neighbor, 15
NNEI, 15–16, 18–20, 151
query points, 15–17
300 IndexRadial Basis, 15
RBAS, 15–21, 151, 153
supporting point, 15–16
N
Newton-Raphson method, 110, 136
noises, 14
nonhomogeneity, 14
nonhomogeneous, 1, 8, 9–21, 151, 187
O
organic matrix, 5
orientation, 25, 46, 69–70, 72, 78
orthotropic, 24, 133
Osteoarthritis, 120–121
osteons, 37, 40–41
Osteoporosis, 35–36
P
periodontal ligament (PDL), 1, 43, 61, 63–66
plane strain, 37, 102
plaque, 163–167
plastic strain, 154–156, 166–167
poroelasticity
Biot coefficient, 101
Biot effective stress, 101
Biot’s consolidation theory, 101
biphasic, 101, 108, 111–112, 130
CPT, 101–102, 110, 130, 136, 187
Darcy’s Law, 101
permeability, 101, 102, 108, 109, 187, 188
pore pressure, 101–102, 105–107, 109–112,
113, 134, 136, 137
porosity, 5, 8
porous media, 2, 101–113, 130, 133,
137, 187
Prager-Lode type, 160
principal directions, 27
principal stresses, 25, 27, 29
prosthesis, 9, 161, 178
R
rigid body motion, 55, 105
S
shape functions, 33
skull, 102, 104–105, 117
shape memory alloy (SMA), 149, 157–167
austenite, 160
martensite, 158, 160
phase transformation, 157, 159–160, 167
shape memory effect, 157–158, 161,
163, 167
superelastic effect, 157
superelasticity, 157–159, 163, 167
SMART, 2, 149, 177–178, 180, 183–184, 188
soft tissues, 1–2, 9, 45–48, 49–57, 61–67, 69,
73, 93–98, 101–113, 130, 136,
137–138, 187–188
SpaceClaim, 52, 179
springs, 141, 143–146
stiffness, 8, 23, 157, 187
strain energy potential, 85, 88, 93
swelling, 56, 70, 73
T
talar component, 2, 18, 149, 151–156, 187
Taylor series, 95
tendon, 8, 120
tension only, 71–73, 84
tetrahedral elements, 151
Thermal expansion coefficient, 70
tibia, 85–87, 120, 125–132, 134, 141,
143–144
time-dependent, 46–47, 61
U
USERMAT, 2, 93–98
V
viscoelasticity, 1, 61, 65, 88, 108
creep, 1–2, 61, 63, 65, 108, 111
Maxwell model, 61–63
Prony series, 61–65
von Mises strain, 88–89
von Mises stresses, 29–30, 40–41, 56–57, 66,
74, 78, 80, 88–89, 98, 127, 128–129,
138, 145, 154–155, 166–167
W
wear, 1–2, 149, 169–170, 171, 172–175, 188,
205, 211
Archard Wear Model, 2, 149, 169, 171
coefficient of friction, 45, 117, 156
wear coefficient, 169, 171–172
Index 301X
XFEM, 1, 33–36, 38, 41, 177, 184, 188
enrichment, 33, 40
Phantom-node method, 33–35, 38
Singularity-based method, 33–34
Y
yield stress, 153, 155–156
Young’s modulus
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