Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation

Citation

Özkaya, N., Leger, D., Goldsheyder, D., & Nordin, M. (2017). Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation (4th ed.). Springer.

Chapter Summary

The fourth edition has about 450 pages: fifteen chapters that move from statics through dynamics to the mechanics of deformable bodies, followed by three mathematical appendices (plane geometry, vector algebra and calculus) and an index. The publisher describes it as integrating statics, dynamics and strength of materials with examples from biology and medicine, extensively revised from the third edition, with many worked examples and over 100 new problems with solutions and illustrations. Chapters end with exercise problems, many with answers, and references.

Chapter 1: Introduction

Places biomechanics within mechanics, from Galileo and Newton to engineering mechanics, and sets out the basic concepts the rest of the book uses: Newton's laws, dimensions and units.

Chapters 2–3: Force Vector; Moment and Torque Vectors

The mathematical tools of statics: forces as vectors and their components and resultants, then moments and torques, couples and their calculation. Vector algebra is supported by an appendix.

Chapter 4: Statics: Systems in Equilibrium

Newton's laws restated for equilibrium, including the rotational form of the second law, the conditions for translational and rotational equilibrium and free-body diagrams as the basis for solving static problems.

Chapter 5: Applications of Statics to Biomechanics

The longest of the statics chapters. It describes the types of skeletal joints and the role of muscles, then works through static analyses of individual joints, ending with the knee and the ankle, where joint reaction forces and muscle forces are calculated from body weight and posture.

Chapter 6: Introduction to Dynamics

A short chapter that introduces kinematics and kinetics before the dynamics chapters that follow.

Chapters 7–8: Linear Kinematics; Linear Kinetics

Chapter 7 covers position, velocity and acceleration in one and two dimensions, including projectile motion applied to ski jumping, diving, gymnastics and throwing events. Chapter 8 applies Newton's second law through equations of motion, and introduces work, energy and power, illustrated repeatedly by a ski jumper on a track.

Chapters 9–10: Angular Kinematics; Angular Kinetics

The rotational counterparts: angular displacement, velocity and acceleration, then torque, mass moment of inertia and rotational equations of motion, with examples such as the forces at the knee during a seated leg-extension exercise.

Chapter 11: Impulse and Momentum

Linear and angular impulse and momentum, collisions (including elastic and elastoplastic collisions and collisions in two dimensions), and the kinetics of rigid bodies in plane motion.

Chapter 12: Introduction to Deformable Body Mechanics

A short transition from rigid bodies to materials that deform under load.

Chapter 13: Stress and Strain

Uniaxial tension testing, load–elongation and stress–strain diagrams, simple stress and strain, elastic deformation and Hooke's law, plastic deformation and necking, strain energy, strain hardening and hysteresis, and the material properties read from stress–strain curves. An example follows force transfer through the fixation device of a fractured femur.

Chapter 14: Multiaxial Deformations and Stress Analyses

The longest chapter on materials: multiaxial stress, principal stresses and Mohr's circle, failure theories, allowable stress and factor of safety, factors affecting strength, fatigue and endurance, stress concentration, torsion and bending.

Chapter 15: Mechanical Properties of Biological Tissues

Viscoelasticity and its spring-and-dashpot models (Kelvin–Voigt, Maxwell and standard solid), creep and time-dependent response, and a comparison of elasticity and viscoelasticity, followed by the mechanical properties of bone (with its dependence on strain rate and bone type) and of tendons and ligaments.

Key Concepts

Chapters 1–5: Statics

• Vectors, moments and torques: the representation of forces and their turning effects, the language of all later analysis.
• Free-body diagram: isolating a body or segment and showing every force acting on it, the first step in every problem.
• Equilibrium: the conditions that net force and net moment are zero, used to find unknown muscle and joint forces.
• Joint reaction force: the force transmitted between bones at a joint, which can be well above body weight.

Chapters 6–11: Dynamics

• Kinematics versus kinetics: describing motion as opposed to relating it to its causes.
• Projectile motion: the trajectory of a body moving under gravity alone, applied to jumps and throws.
• Work–energy and impulse–momentum methods: alternatives to the equations of motion for problems involving speeds and collisions.
• Mass moment of inertia: resistance to angular acceleration, central to rotational kinetics.

Chapters 12–15: Deformable bodies

• Stress and strain: internal force per unit area and relative deformation, linked by Hooke's law in the elastic range.
• Mohr's circle: a graphical method for finding principal and maximum shear stresses.
• Fatigue and stress concentration: why repeated or localised loads cause failure below the static strength.
• Viscoelasticity: the time- and rate-dependent behaviour of tissues, modelled with springs and dashpots.

Critical Analysis

Strengths

• One consistent mechanics course. The book covers statics, dynamics and strength of materials in a single sequence, each part beginning with a short introductory chapter, so students without an engineering background meet the whole of elementary mechanics in one place.
• Worked examples with biological settings. Joint analyses of the knee and ankle, a seated knee-extension exercise, ski jumping, fracture fixation and tissue testing appear as worked examples and problems. The publisher counts over 100 new problem sets with solutions in this edition, and answers are given to many problems.
• Self-contained mathematics. Appendices on plane geometry, vector algebra and calculus let readers refresh the mathematics without another text; the publisher states that no advanced mathematical background is needed.
• A proper introduction to tissue mechanics. Chapter 15 introduces viscoelastic models and the behaviour of bone, tendon and ligament, preparing students for more advanced texts.

Limitations

• Mechanics first, biology light. Anatomy enters mainly through Chapter 5's joint descriptions and Chapter 15; physiology of muscle and neural control is not a topic, and there is no fluid mechanics, so blood flow and cardiovascular biomechanics are absent.
• Quasi-static joint models. The biomechanical applications concentrate on simplified two-dimensional static analyses; there is little on motion capture, inverse dynamics with measured data or computer modelling.

Where It Fits in the Course

Özkaya and colleagues sit between the conceptual and the advanced books in this course. Duane Knudson's Fundamentals of Biomechanics teaches human-movement biomechanics through nine qualitative principles and algebra-level calculation; students in kinesiology may start there and turn to Özkaya when they need to set up and solve force problems. Ethier and Simmons's Introductory Biomechanics: From Cells to Organisms assumes the solid mechanics that Özkaya teaches and adds fluid mechanics, cell mechanics and organ systems, so it is a natural next book.

Humphrey and O'Rourke's An Introduction to Biomechanics develops continuum mechanics for solids and fluids, and Y. C. Fung's Biomechanics: Mechanical Properties of Living Tissues is the graduate treatment of constitutive behaviour that Chapter 15 introduces. Peterson and Bronzino's Biomechanics: Principles and Applications is an edited reference for specific topics.

How to Use This Book

The book suits undergraduates in biomedical engineering, and students of physical therapy, occupational therapy, ergonomics, orthopaedics and sports medicine who need quantitative biomechanics. Algebra, trigonometry and introductory calculus are needed; the appendices review them. Basic physics and anatomy help but are not assumed in depth.

A practical plan:

• Statics core: Chapters 1–5 in order. Do not skip Chapters 2–3 even with prior physics, since the vector methods are used throughout; Chapter 5 is where the mechanics becomes biomechanics.
• Dynamics: Chapters 6–11. Courses short of time can take Chapters 7–10 and treat Chapter 11 (collisions) as optional.
• Deformable bodies: Chapters 12–13 are essential; Chapter 14 can be selective (Mohr's circle, fatigue, bending and torsion); Chapter 15 is the bridge to tissue mechanics and should not be skipped.

Solve problems after each section rather than at the end of a chapter, always drawing a free-body diagram first, and check answers where they are given. Students heading into biomechanics research should follow the book with a text on fluid and continuum mechanics.