Preface
Chapter 1 Introduction
1.1 Finite element method and analysis
1.2 Calculation of strain and stress from the FE model
1.2.1 Average strain and point strain
1.2.2 Normal and shear strain
1.2.3 Calculation of stress
1.3 Sample matrix structural analysis
1.3.1 Element stiffness matrix of a linear spring
1.3.2 Element stiffness matrix of a linear spring not in line with the x-axis
1.3.3 Element stiffness matrix of a homogeneous linear elastic bar
1.3.4 Global stiffness matrix of multiple inline linear springs or bars
1.3.5 Global stiffness matrix of a simple biomechanics problem
1.3.6 Global stiffness matrix of a simple truss bridge
1.3.7 Gaussian or Gauss elimination
1.4 From MSA to a finite element model
1.5 Exercises
Chapter 2 Meshing, Element Types, and Element Shape Functions
2.1 Structure idealization and discretization
2.2 Node
2.3 Element
2.3.1 Simplest element types
2.3.2 1D element type
2.3.3 2D element type
2.3.4 3D element type
2.4 Formation of finite element mesh
2.5 Element shape functions and [B] matrix
2.5.1 1D 2-node element shape functions
2.5.2 2D 3-node linear triangular and 4-node bilinear plane stress quadrilateral elements
2.5.3 2D, 4-node plate element shape functions
2.5.4 3D, 4-node shell element
2.5.5 3D, 8-node trilinear element shape functions
2.6 Exercises
Chapter 3 Isoparametric Formulation and Mesh Quality
3.1 Introduction
3.2 Natural coordinate system
3.3 Isoparametric formulation of 1D elements
3.3.1 1D linear bar element isoparametric shape functions
3.3.2 1D beam element isoparametric shape functions
3.4 Isoparametric formulation of 2D element
3.4.1 Isoparametric formulation of 2D triangular element
3.4.2 Isoparametric formulation of 2D bilinear element
3.5 Isoparametric formulation of 3D element
3.5.1 Constant strain tetrahedral element
3.5.2 Trilinear hexahedral element
3.6 Transfer mapping function
3.7 Jacobian matrix and determinant of Jacobian matrix
3.8 Element Quality (Jacobian, warpage, aspect ratio, etc.)
3.8.1 Normalized Jacobian
3.8.2 Internal and skew angles
3.8.3 Warpage
3.8.4 Aspect ratio
3.8.5 Distortion
3.8.6 Stretch
3.8.7 Generation of high quality mesh
3.8.8 Patch test
3.9 Exercises
Chapter 4 Element Stiffness Matrix
4.1 Introduction
4.2 Direct method
4.2.1 Direct formation of structure stiffness matrix
4.2.2 Direct method for a 2-node beam element
4.3 Strong formulation
4.4 Weak formulation
4.4.1 Variational method
4.4.2 Weight residual method
4.5 Derive element stiffness matrix from shape functions
4.5.1 Gauss Quadrature
4.5.2 1D element stiffness matrix using Gauss quadrature
4.5.3 Gauss integration points for 2D and 3D elements
4.5.4 2D element stiffness matrix using Gauss quadrature
4.5.5 Full and reduced integration
4.5.6 Zero-energy mode
4.6 Method of superposition
4.6.1 Stiffness matrix of a 2D frame element
4.6.2 Stiffness matrix of a 3D frame element
4.7 Coordinate transformation
4.7.1 2D rotation of a vector
4.7.2 2D rotation of the stiffness matrix
4.7.3 3D rotation
4.8 Exercises
Chapter 5 Material Laws and Properties
5.1 Material Laws
5.1.1 Linear elastic material
5.1.2 Elastic plastic material
5.1.3 Hyperelastic material
5.1.4 Viscoelastic material
5.1.5 Orthotropic material
5.1.6 Foam material
5.1.7 Material defined by equation of state
5.2 Material Test Strategy and Associated Property
5.2.1 Experimental types for biological tissue testing
5.2.2 Reverse engineering methodology
5.2.3 List of common material properties of biological tissues
Chapter 6 Boundary and loading conditions
6.1 Essential and natural boundary conditions
6.2 Nodal constraint and prescribed displacement
6.2.1 Nodal constraint
6.2.2 Prescribed displacement
6.2.3 Penalty method
6.2.4 Symmetrical FE modeling through nodal constraint
6.3 Natural boundary/loading conditions
6.3.1 Concentrated loads
6.3.2 Distributed load
6.3.3 Initial velocity and acceleration
6.4 Exercises
Chapter 7 Stepping through finite element analysis
7.1 Introduction
7.2 Gaussian elimination and iterative procedures
7.2.1 Jacobi or simultaneous displacement method
7.2.2 Gauss-Seidel or successive displacement method
7.3 Verification and validation
7.3.1 Historical aspect
7.3.2 Verification
7.3.3 Validation
7.3.4 Quantifying the extent of validation
7.3.5 Uncertainty Qualification
7.4 Response Variables
7.5 Parametric studies
7.6 Design of computer experiments
7.7 Stochastic simulation versus Monte Carlo simulation
Chapter 8 Modal and Transient Dynamic Solutions
8.1 Mass calculation
8.2 Central difference time integration method
8.3 Implicit modal analysis and explicit transient dynamic FE solutions
8.4 Common problems encountered
8.4.1 Over and under constraints
8.4.2 Negative volume
8.4.3 Hourglass energy and prevention
8.4.4 Fail to detect contact
8.5 Failure simulation
8.5.1 Strain criteria based failure simulations
8.5.2 Spot weld force based failure simulations
Chapter 9 Biological Components Modeling
9.1 Convert biomedical images to finite element mesh
9.1.1 Anatomical components
9.1.2 Biomedical Imaging
9.1.3 Registration and Segmentation
Chapter 10 Parametric Modeling
10.1 Methods to morph subject-specific FE mesh for other anthropometries
10.2 Modeling the obese subject
Chapter 11 Modeling passive and active muscle
11.1 Introduction
11.2 Methods for modeling passive muscle
11.3 Methods for modeling muscular activation
11.4 Application of muscle models
Chapter 12 Modeling the Head
12.1 Introduction of corresponding anatomy
12.2 Injury mechanism
12.3 Material models
12.4 Material properties
12.5 Test data available for model validation
12.6 Concluding remarks
Chapter 13 Modeling the Neck
13.1 Introduction of corresponding anatomy
13.2 Injury mechanism
13.3 Material models
13.4 Material properties
13.5 Test data available for model validation
13.6 Concluding remarks
Chapter 14 Modeling the Upper Torso and Upper Extremity
14.1 Introduction of corresponding anatomy
14.2 Injury mechanism
14.3 Material models
14.4 Material properties
14.5 Test data available for model validation
14.6 Concluding remarks
Chapter 15 Modeling the Lower Torso
15.1 Introduction of corresponding anatomy
15.2 Injury mechanism
15.3 Material models
15.4 Material properties
15.5 Test data available for model validation
15.6 Concluding remarks
Chapter 16 Modeling the Lower Extremity
16.1 Introduction of corresponding anatomy
16.2 Injury mechanism
16.3 Material models
16.4 Material properties
16.5 Test data available for model validation
16.6 Concluding remarks
Chapter 17 Modeling Vulnerable subjects
17.1 Modeling pediatric subjects
17.2 Modeling elderly female subjects
Chapter 18 Fundamental of Blast Modeling
18.1 Friedlander blast wave
18.2 Equation of state
18.3 Coupling fluid and solid interfaces
18.4 Primary blast induced head injuries
