This book covers the fundamentals of biomechanics. Topics include bio solids, biofluids, stress, balance and equilibrium. Students are encouraged to contextualize principles and exercises within a "big picture" of biomechanics. This is an ideal book for undergraduate students with interests in biomedical engineering.

Table of Contents

• Dedication
• Preface to the Second Edition
• Preface to the First Edition
• Comments from a Student to a Student
• Acknowledgments
• 1. Introduction
• 1.1 Point of Departure
• 1.2 Health Care Applications
• 1.3 What Is Continuum Mechanics?
• 1.4 A Brief on Cell Biology
• 1.5 The Extracellular Matrix
• 1.6 Mechanotransduction in Cells
• 1.7 General Method of Approach
• Chapter Summary
• Appendix 1: Engineering Statics
• Exercises
• Part I Background
• 2. Stress, Strain, and Constitutive Relations
• 2.1 Introduction
• 2.2 Concept of Stress
• 2.3 Stress Transformations
• 2.4 Principal Stresses and Maximum Shear
• 2.5 Concept of Strain
• 2.6 Constitutive Behavior
• 2.6.1 Illustrative Characteristic Behaviors
• 2.6.2 Hookean LEHI Behavior
• 2.6.3 Hooke ’ s Law for Transverse Isotropy
• 2.6.4 Hooke ’ s Law for Orthotropy
• 2.6.5 Other Coordinate Systems
• 2.7 Mechanical Properties of Bone
• Chapter Summary
• Appendix 2: Material Properties
• Exercises
• Part II Biosolid Mechanics
• 3. Equilibrium, Universal Solutions, and Inflation
• 3.1 General Equilibrium Equations
• 3.2 Navier–Space Equilibrium Equations
• 3.3 Axially Loaded Rods
• 3.3.1 Biological Motivation
• 3.3.2 Mathematical Formulation
• 3.4 Pressurization and Extension of a Thin-Walled Tube
• 3.4.1 Biological Motivation
• 3.4.2 Mathematical Formulation
• 3.5 Pressurization of a Thin Spherical Structure
• 3.5.1 Biological Motivation
• 3.5.2 Mathematical Formulation
• 3.6 Thick-Walled Cylinders
• Chapter Summary
• Appendix 3: First Moments of Area
• Exercises
• 4. Extension and Torsion
• 4.1 Deformations Due to Extension
• 4.1.1 Biological Motivation
• 4.1.2 Theoretical Framework
• 4.1.3 Clinical Application
• 4.2 Shear Stress Due to Torsion
• 4.2.1 Introduction
• 4.2.2 Biological Motivation
• 4.2.3 Mathematical Formulation
• 4.3 Principal Stresses and Strains in Torsion
• 4.4 Angle of Twist Due to Torque
• 4.4.1 Basic Derivation
• 4.4.2 Statically Indeterminate Problems
• 4.5 Experimental Design: Bone Properties
• 4.6 Experimental Design: Papillary Muscles
• 4.6.1 Biological Motivation
• 4.6.2 Experimental Design
• 4.7 Inflation, Extension, and Twist
• Chapter Summary
• Appendix 4: Second Moments of Area
• Exercises
• 5. Beam Bending and Column Buckling
• 5.1 Shear Forces and Bending Moments
• 5.2 Stresses in Beams
• 5.2.1 Biological Motivation
• 5.2.2 Theoretical Framework
• 5.2.3 Illustrative Examples
• 5.3 Deformation in Beams
• 5.3.1 Biological Motivation
• 5.3.2 Theoretical Framework
• 5.3.3 Illustrative Examples
• 5.4 Transducer Design: The AFM
• 5.4.1 Introduction
• 5.4.2 The Atomic Force Microscope
• 5.4.3 Illustrative Example
• 5.5 Principle of Superposition
• 5.6 Column Buckling
• 5.6.1 Concept of Stability
• 5.6.2 Buckling of a Cantilevered Column
• Chapter Summary
• Appendix 5: Parallel Axis Theorem and Composite Sections
• Exercises
• 6. Some Nonlinear Problems
• 6.1 Kinematics
• 6.2 Pseudoelastic Constitutive Relations
• 6.3 Design of Biaxial Tests on Planar Membranes
• 6.3.1 Biological Motivation
• 6.3.2 Theoretical Framework
• 6.4 Stability of Elastomeric Balloons
• 6.4.1 Biological Motivation
• 6.4.2 Theoretical Framework
• 6.4.3 Inflation of a Neuroangioplasty Balloon
• 6.5 Residual Stress and Arteries
• 6.5.1 Biological Motivation
• 6.5.2 Theoretical Framework
• 6.5.3 Illustrative Results
• 6.6 A Role of Vascular Smooth Muscle
• 6.6.1 Muscle Basics
• 6.6.2 Quantification
• Chapter Summary
• Appendix 6: Matrices
• Exercises
• 7. Stress, Motion, and Constitutive Relations
• 7.1 Introduction
• 7.2 Stress and Pressure
• 7.3 Kinematics: The Study of Motion
• 7.3.1 Velocity and Acceleration
• 7.3.2 Fluid Rotation
• 7.3.3 Rate of Deformation
• 7.4 Constitutive Behavior
• 7.4.1 Newtonian Behavior
• 7.4.2 Non-Newtonian Behavior
• 7.5 Blood Characteristics
• 7.5.1 Plasma
• 7.5.2 Blood Cells
• 7.5.3 Additional Rheological Considerations
• 7.6 Cone-and-Plate Viscometry
• Chapter Summary
• Appendix 7: Vector Calculus Review
• Exercises
• Part III Biofluid Mechanics 351
• 8. Fundamental Balance Relations
• 8.1 Balance of Mass
• 8.2 Balance of Linear Momentum
• 8.3 Navier–Stokes Equations
• 8.4 The Euler Equation
• 8.5 The Bernoulli Equation
• 8.5.1 Bernoulli Equation for Flow Along a Streamline
• 8.5.2 Bernoulli Equation for Irrotational Flow
• 8.5.3 Further Restrictions for the Bernoulli Equation
• 8.6 Measurement of Pressure and Flow
• 8.6.1 Pressure
• 8.6.2 Flow
• 8.7 Navier–Stokes Worksheets
• Chapter Summary
• Appendix 8: Differential Equations
• Exercises
• 9. Some Exact Solutions
• 9.1 Flow Between Parallel Flat Plates
• 9.1.1 Biological Motivation
• 9.1.2 Mathematical Formulation
• 9.2 Steady Flow in Circular Tubes
• 9.2.1 Biological Motivation
• 9.2.2 Mathematical Formulation
• 9.3 Circumferential Flow Between Concentric Cylinders
• 9.3.1 Bioreactor Application
• 9.3.2 Mathematical Formulation
• 9.3.3 Viscometer Application
• 9.4 Steady Flow in an Elliptical Cross Section
• 9.4.1 Biological Motivation
• 9.4.2 Mathematical Formulation
• 9.5 Pulsatile Flow
• 9.5.1 Some Biological Motivation
• 9.5.2 Mathematical Formulation
• 9.6 Non-Newtonian Flow in a Circular Tube
• 9.6.1 Motivation
• 9.6.2 Mathematical Formulation
• Chapter Summary
• Appendix 9: Biological Parameters
• Exercises
• 10. Control Volume and Semi-empirical Methods
• 10.1 Fundamental Equations
• 10.1.1 Theoretical Framework
• 10.1.2 Special Cases for Mass and Momentum
• 10.1.3 The Energy Equation
• 10.2 Control Volume Analyses in Rigid Conduits
• 10.2.1 Clinical Motivation
• 10.2.2 Illustrative Examples
• 10.3 Control Volume Analyses in Deforming Containers
• 10.3.1 Clinical Motivation
• 10.3.2 Mathematical Formulation
• 10.4 Murray ’ s Law and Optimal Design
• 10.4.1 Straight Segment
• 10.4.2 Bifurcation Areas
• 10.4.3 Bifurcation Patterns
• 10.5 Buckingham Pi and Experimental Design
• 10.5.1 Motivation
• 10.5.2 Recipe
• 10.6 Pipe Flow
• 10.7 Conclusion
• Chapter Summary
• Appendix 10: Thermodynamics
• Exercises
• 11. Coupled Solid–Fluid Problems
• 11.1 Vein Mechanobiology
• 11.1.1 Biological Motivation
• 11.1.2 Theoretical Framework
• 11.2 Diffusion Through a Membrane
• 11.2.1 Biological Motivation
• 11.2.2 Theoretical Basis
• 11.2.3 Illustration
• 11.3 Dynamics of a Saccular Aneurysm
• 11.3.1 Biological Motivation
• 11.3.2 Mathematical Framework
• 11.4 Viscoelasticity: QLV and Beyond
• 11.4.1 Linearized Viscoelasticity
• 11.4.2 Quasilinear Viscoelasticity
• 11.4.3 Need for Nonlinear Theories
• 11.5 Lubrication of Articulating Joints
• 11.5.1 Biological Motivation
• 11.5.2 Hydrodynamic Lubrication
• 11.5.3 Need for a Mixture Theory
• 11.6 Thermomechanics, Electromechanics, and Chemomechanics
• Chapter Summary
• Appendix 11: Wave Equations
• Exercises
• Part IV Closure
• 12. Epilogue
• 12.1 Future Needs in Biomechanics
• 12.2 Need for Lifelong Learning
• 12.3 Conclusion
• References
• About the Authors