Biomechanics: Concepts and Computation

✍ Scribed by Cees Oomens, Marcel Brekelmans, Frank Baaijens

• Publisher: Cambridge University Press
• Year: 2009
• Tongue: English
• Leaves: 348
• Series: Cambridge Texts in Biomedical Engineering
• Edition: 1
• Category: Library

✦ Synopsis

This is the first textbook that integrates both general and specific topics, theoretical background and biomedical engineering applications, as well as analytical and numerical approaches. This quantitative approach integrates the classical concepts of mechanics and computational modelling techniques, in a logical progression through a wide range of fundamental biomechanics principles. Online MATLAB-based software along with examples and problems using biomedical applications will motivate undergraduate biomedical engineering students to practice and test their skills. The book covers topics such as kinematics, equilibrium, stresses and strains, and also focuses on large deformations and rotations and non-linear constitutive equations, including visco-elastic behaviour and the behaviour of long slender fibre-like structures. This is the definitive textbook for students.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
About the cover......Page 13
Preface......Page 15
1.3 Vector operations......Page 17
1.4 Decomposition of a vector with respect to a basis......Page 21
Exercises......Page 24
2.2 Definition of a force vector......Page 26
2.3 Newton’s Laws......Page 28
2.4 Vector operations on the force vector......Page 29
2.5 Force decomposition......Page 30
2.6 Representation of a vector with respect to a vector basis......Page 33
2.7 Column notation......Page 37
2.8 Drawing convention......Page 40
2.9 The concept of moment......Page 41
2.10 Definition of the moment vector......Page 42
2.11 The two-dimensional case......Page 45
2.12 Drawing convention of moments in three dimensions......Page 48
Exercises......Page 49
3.2 Static equilibrium conditions......Page 53
3.3 Free body diagram......Page 56
Exercises......Page 63
4.2 Elastic fibres in one dimension......Page 66
4.3 A simple one-dimensional model of a skeletal muscle......Page 69
4.4 Elastic fibres in three dimensions......Page 71
4.5 Small fibre stretches......Page 77
Exercises......Page 82
5.1 Introduction......Page 85
5.2 Viscous behaviour......Page 87
5.2.1 Small stretches: linearization......Page 89
5.3.1 Continuous and discrete time models......Page 90
5.3.2 Visco-elastic models based on springs and dashpots: Maxwell model......Page 94
5.3.3 Visco-elastic models based on springs and dashpots: Kelvin–Voigt model......Page 98
5.4.1 The Storage and the Loss Modulus......Page 99
5.4.2 The Complex Modulus......Page 101
5.4.3 The standard linear model......Page 103
5.5 Appendix: Laplace and Fourier transforms......Page 108
Exercises......Page 110
6.2 Equilibrium in a subsection of a slender structure......Page 115
6.3 Stress and strain......Page 117
6.5 Deformation of an inhomogeneous bar......Page 120
Exercises......Page 127
7.1 Introduction......Page 130
7.2 Orientation in space......Page 131
7.3 Mass within the volume V......Page 133
7.4 Scalar fields......Page 136
7.5 Vector fields......Page 138
7.6 Rigid body rotation......Page 141
7.7 Some mathematical preliminaries on second-order tensors......Page 143
Exercises......Page 146
8.1 Stress vector......Page 148
8.2 From stress to force......Page 149
8.3 Equilibrium......Page 150
8.4 Stress tensor......Page 158
8.5 Principal stresses and principal stress directions......Page 162
8.6 Mohr’s circles for the stress state......Page 165
8.8 Equivalent stress......Page 166
Exercises......Page 168
9.2 Geometrical description of the material configuration......Page 172
9.3 Lagrangian and Eulerian description......Page 174
9.4 The relation between the material and spatial time derivative......Page 175
9.5 The displacement vector......Page 177
9.6 The gradient operator......Page 178
9.7 Extra displacement as a rigid body......Page 180
9.8 Fluid flow......Page 182
Exercises......Page 183
10.2 A material line segment in the reference and current configuration......Page 186
10.3 The stretch ratio and rotation......Page 189
10.4 Strain measures and strain tensors and matrices......Page 192
10.6 Deformation rate and rotation velocity......Page 196
Exercises......Page 199
11.2 The local balance of mass......Page 202
11.3 The local balance of momentum......Page 203
11.4 The local balance of mechanical power......Page 205
11.5 Lagrangian and Eulerian description of the balance equations......Page 206
Exercises......Page 208
12.1 Introduction......Page 210
12.2 Elastic behaviour at small deformations and rotations......Page 211
12.3 The stored internal energy......Page 214
12.4 Elastic behaviour at large deformations and/or large rotations......Page 216
12.5 Constitutive modelling of viscous fluids......Page 219
12.6 Newtonian fluids......Page 220
12.8 Diffusion and filtration......Page 221
Exercises......Page 222
13.2 Solution strategies for deforming solids......Page 226
13.2.1 General formulation for solid mechanics problems......Page 227
13.2.2 Geometrical linearity......Page 228
13.2.4 Linear elasticity theory, static......Page 229
13.2.5 Linear plane stress theory, static......Page 230
13.2.6 Boundary conditions......Page 234
13.3 Solution strategies for viscous fluids......Page 236
13.3.2 The equations for a Newtonian fluid......Page 237
13.3.3 Stationary flow of an incompressible Newtonian fluid......Page 238
13.3.5 Elementary analytical solutions......Page 239
13.4 Diffusion and filtration......Page 241
Exercises......Page 243
14.1 Introduction......Page 248
14.2 The diffusion equation......Page 249
14.3 Method of weighted residuals and weak form of the model problem......Page 251
14.4 Polynomial interpolation......Page 253
14.5 Galerkin approximation......Page 255
14.7 Isoparametric elements and numerical integration......Page 262
14.8 Basic structure of a finite element program......Page 266
14.9 Example......Page 269
Exercises......Page 272
15.2 The convection-diffusion equation......Page 280
15.3 Temporal discretization......Page 282
15.4 Spatial discretization......Page 285
Exercises......Page 289
16.1 Introduction......Page 293
16.2 Diffusion equation......Page 294
16.3 Divergence theorem and integration by parts......Page 295
16.5 Galerkin discretization......Page 296
16.6 Convection-diffusion equation......Page 299
16.7 Isoparametric elements and numerical integration......Page 300
16.8 Example......Page 304
Exercises......Page 307
17.1 Introduction......Page 311
17.2 Isoparametric, bilinear quadrilateral element......Page 313
17.3 Linear triangular element......Page 315
17.4 Lagrangian and Serendipity elements......Page 318
17.4.1 Lagrangian elements......Page 319
17.4.2 Serendipity elements......Page 320
17.5 Numerical integration......Page 321
Exercises......Page 325
18.2 Linear elasticity......Page 329
18.3 Weak formulation......Page 331
18.4 Galerkin discretization......Page 332
18.6 Example......Page 338
Exercises......Page 340
References......Page 345
Index......Page 347

✦ Subjects

Биологические дисциплины;Биомеханика;