1 Nomenclature
2 Dynamics
2.1 Kinematics
2.1.1 Extensive and intensive properties
2.1.2 Notation and conventions
2.1.3 Reynolds transport theorem of a moving control volume
2.1.4 The material derivative of an extensive property
2.2 Conservation of mass
2.3 Equations of motion
2.3.1 Coordinate stresses
2.3.2 Example 1: Uniaxial state of stress
2.3.3 Example 2: Pure shear stress state
2.3.4 Cauchy's stress theorem and the Cauchy stress tensor
2.3.5 Example 3: Example: Fluid at rest: Isotropic state of stress
2.4 Cauchy's equations of motion
2.4.1 Derivation of Cauchy's equations of motion
2.4.2 Example 4: The hydrostatic pressure distribution
2.4.3 Example 5: Cauchy equations in cylindrical coordinates
2.5 Stress analysis
2.5.1 Principal stresses
2.5.2 Maximum shear stress
2.5.3 Planar stress
2.5.4 Example 6: Biaxial state of stress for thin-walled structures
3 Deformation
3.1 Measures of strain
3.2 The Green strain tensor
3.3 Small strains and small deformations
3.3.1 Small strains
3.3.2 Small deformations
3.3.3 Principal strains
3.3.4 Small strains in a surface
3.3.5 Example 7: Strain rosettes
3.4 Strain rates and rates of rotation
3.4.1 Example 8: Simple shear flow. Rectilinear rotational flow
4 Elasticity
4.0.1 Fundamental properties of elastic materials
4.1 Isotropic and linearly elastic materials
4.1.1 The Hookean solid
4.1.2 Navier equations
4.1.3 2D theory of elasticity
4.1.4 Example 9: Spherical shell of steel
4.1.5 Plane displacement
4.1.6 Example 10: Plane displacements for a thick walled cylinder
4.2 Mechanical energy balance
4.3 Hyperelastic materials and strain energy
4.3.1 Hyperelasticity for large derformations
4.3.2 Stress tensors for large deformations
4.3.3 Isotropic hyperelastic materials
4.3.4 Example 11: Thin sheet of incompressible material
4.3.5 Example 12: The Mooney-Rivlin material
4.4 Anisotropic Materials
4.5 Waves in elastic materials
4.5.1 Plane elastic waves
Exercise 1: The generalized Hooke's law
Exercise 2: Invariants
Exercise 3: Shear modulus
5 Fluid mechanics
5.1 Introduction
5.1.1 Fundamental concepts in fluid mechanics
5.2 Conservation of mass
5.3 Inviscid fluids
5.3.1 Example 13: Sound waves
5.4 Linear viscous fluids
5.4.1 Simple shear flow
5.4.2 The Navier-Stokes equations
5.4.3 About the NS equations
5.4.4 Example 14: Flow between parallel planes
5.4.5 Example 15: Laminar pipe flow
5.5 Generalized Newtonian model
5.5.1 Example 16: Stationary pipeflow for GNF
5.5.2 Example 17: Power law for steady pipeflow
5.6 Pulsatile flow in straight tubes
5.6.1 Straight tube velocity profiles
5.6.2 Wall shear stress for pulsatile flow in straight tubes
5.6.3 Longitudinal impedance for pulsatile flow in straight tubes
6 The cardiovascular system
6.1 Pressure and flow in the cardiovascular system
6.1.1 Arterial anatomy
6.1.2 Compliance and distensibility
6.1.3 Mathematical representation of periodic pressure and flow
6.1.4 Vascular impedance
6.2 Lumped models
6.2.1 The Windkessel model
6.2.2 The three-element Windkessel model
6.2.3 Methods for estimation of total arterial compliance
6.2.4 Example 18: Estimation of total arterial compliance with the TDM method
Exercise 4: Windkessel model
7 Blood flow in compliant vessels
7.1 Poiseuille flow in a compliant vessel
7.2 Infinitesimal derivation of the 1D governing equations for a compliant vessel
7.2.1 Conservation of mass
7.2.2 The momentum equation
7.3 Integral derivation of the 1D governing equations for a compliant vessel
7.3.1 1D transport equation
7.3.2 Mass conservation
7.3.3 Momentum equation
7.3.4 Example 19: Momentum equations for invicid flow
7.3.5 Example 20: Momentum equations for polynomial velocity profiles
7.3.6 Linearized and inviscid wave equations
7.3.7 Characteristic impedance
7.3.8 Progressive waves superimposed on steady flow
7.4 Input impedance
7.5 Wave reflections
7.6 General equations with reflection and friction
7.7 Wave separation
7.8 Wave travel and reflection
7.9 Networks 1D compliant vessels
7.9.1 Lumped heart model: varying elastance model
7.9.2 Nonlinear wave separation
7.10 Fluid structure interaction for small deformations in Hookean vessel
7.10.1 The governing equations for the Hookean vessel
7.10.2 The governing equations for the fluid
7.10.3 Coupling of structure and fluid
8 Appendix
8.1 Trigonometric relations
8.2 Vectors
8.3 Orthogonal Coordinates
8.3.1 Gradient, divergence and rotation in general orthogonal coordinates
8.4 Integral Theorems
8.5 Properties of Bessel functions
8.6 Bibliography