Biomechanics: Concepts and Computation | by Cees Oomens, Marcel Brekelmans and Frank Baaijens | 2009 | ISBN: 9780521875585. Biomedical Engineering Books. Mechanical Behaviour of Fibres. Biological Materials and Continuum Mechanics
Biomechanics: Concepts and Computation
by Cees Oomens, Marcel Brekelmans and Frank Baaijens
2009 (346 pages)
ISBN:9780521875585
Using a quantitative biomechanics approach, this book integrates both general and specific topics, theoretical background and biomedical engineering applications, as well as analytical and numerical approaches.
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Biomechanics—Concepts and Computation
About the Cover
Preface
Chapter 1 – Vector Calculus
1.1: Introduction
1.2: Definition of a Vector
1.3: Vector Operations
1.4: Decomposition of a Vector with Respect to a Basis
Exercises
Chapter 2 – The Concepts of Force and Moment
2.1: Introduction
2.2: Definition of a Force Vector
2.3: Newton’s Laws
2.4: Vector Operations on the Force Vector
2.5: Force Decomposition
2.6: Representation of a Vector with Respect to a Vector Basis
2.7: Column Notation
2.8: Drawing Convention
2.9: The Concept of Moment
2.10: Definition of the moment vector
2.11: The Two-Dimensional Case
2.12: Drawing Convention of Moments in Three Dimensions
Exercises
Chapter 3 – Static Equilibrium
3.1: Introduction
3.2: Static Equilibrium Conditions
3.3: Free Body Diagram
Exercises
Chapter 4 – The Mechanical Behaviour of Fibres
4.1: Introduction
4.2: Elastic Fibres in One Dimension
4.3: A Simple One-Dimensional Model of a Skeletal Muscle
4.4: Elastic Fibres in Three Dimensions
4.5: Small Fibre Stretches
Exercises
Chapter 5 – Fibres—Time-Dependent Behaviour
5.1: Introduction
5.2: Viscous Behaviour
5.3: Linear Visco-Elastic Behaviour
5.4: Harmonic Excitation of Visco-Elastic Materials
5.5: Appendix: Laplace and Fourier Transforms
Exercises
Chapter 6 – Analysis of a One-Dimensional Continuous Elastic Medium
6.1: Introduction
6.2: Equilibrium in a Subsection of a Slender Structure
6.3: Stress and Strain
6.4: Elastic Stress–Strain Relation
6.5: Deformation of an Inhomogeneous Bar
Exercises
Chapter 7 – Biological Materials and Continuum Mechanics
7.1: Introduction
7.2: Orientation in Space
7.3: Mass within the Volume V
7.4: Scalar Fields
7.5: Vector Fields
7.6: Rigid Body Rotation
7.7: Some Mathematical Preliminaries on Second-Order Tensors
Exercises
Chapter 8 – Stress in Three-Dimensional Continuous Media
8.1: Stress Vector
8.2: From Stress to Force
8.3: Equilibrium
8.4: Stress Tensor
8.5: Principal Stresses and Principal Stress Directions
8.6: Mohr’s Circles for the Stress State
8.7: Hydrostatic Pressure and Deviatoric Stress
8.8: Equivalent Stress
Exercises
Chapter 9 – Motion—the Time as an Extra Dimension
9.1: Introduction
9.2: Geometrical Description of the Material Configuration
9.3: Lagrangian and Eulerian Description
9.4: The Relation Between the Material and Spatial Time Derivative
9.5: The Displacement Vector
9.6: The Gradient Operator
9.7: Extra Displacement as a Rigid Body
9.8: Fluid Flow
Exercises
Chapter 10 – Deformation and Rotation, Deformation Rate and Spin
10.1: Introduction
10.2: A Material Line Segment in the Reference and Current Configuration
10.3: The Stretch Ratio and Rotation
10.4: Strain Measures and Strain Tensors and Matrices
10.5: The Volume Change Factor
10.6: Deformation Rate and Rotation Velocity
Exercises
Chapter 11 – Local Balance of Mass, Momentum and Energy
11.1: Introduction
11.2: The Local Balance of Mass
11.3: The Local Balance of Momentum
11.4: The Local Balance of Mechanical Power
11.5: Lagrangian and Eulerian Description of the Balance Equations
Exercises
Chapter 12 – Constitutive Modelling of Solids and Fluids
12.1: Introduction
12.2: Elastic Behaviour at Small Deformations and Rotations
12.3: The Stored Internal Energy
12.4: Elastic Behaviour at Large Deformations and/or Large Rotations
12.5: Constitutive Modelling of Viscous Fluids
12.6: Newtonian Fluids
12.7: Non-Newtonian Fluids
12.8: Diffusion and Filtration
Exercises
Chapter 13 – Solution Strategies for Solid and Fluid Mechanics Problems
13.1: Introduction
13.2: Solution Strategies for Deforming Solids
13.3: Solution Strategies for Viscous Fluids
13.4: Diffusion and Filtration
Exercises
Chapter 14 – Solution of the One-Dimensional Diffusion Equation by Means of the Finite Element Method
14.1: Introduction
14.2: The Diffusion Equation
14.3: Method of Weighted Residuals and Weak form of the Model Problem
14.4: Polynomial Interpolation
14.5: Galerkin Approximation
14.6: Solution of the Discrete Set of Equations
14.7: Isoparametric Elements and Numerical Integration
14.8: Basic Structure of a Finite Element Program
14.9: Example
Exercises
Chapter 15 – Solution of the One-Dimensional Convection-Diffusion Equation by Means of the Finite Element Method
15.1: Introduction
15.2: The Convection-Diffusion Equation
15.3: Temporal Discretization
15.4: Spatial Discretization
Exercises
Chapter 16 – Solution of the Three-Dimensional Convection-Diffusion Equation by Means of the Finite Element Method
16.1: Introduction
16.2: Diffusion Equation
16.3: Divergence Theorem and Integration by Parts
16.4: Weak Form
16.5: Galerkin Discretization
16.6: Convection-Diffusion Equation
16.7: Isoparametric Elements and Numerical Integration
16.8: Example
Exercises
Chapter 17 – Shape Functions and Numerical Integration
17.1: Introduction
17.2: Isoparametric, Bilinear Quadrilateral Element
17.3: Linear Triangular Element
17.4: Lagrangian and Serendipity Elements
17.5: Numerical Integration
Exercises
Chapter 18 – Infinitesimal Strain Elasticity Problems
18.1: Introduction
18.2: Linear Elasticity
18.3: Weak Formulation
18.4: Galerkin Discretization
18.5: Solution
18.6: Example
Exercises
References
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