Biomechanics Lecture Notes

BIOMECHANICS SYLLABUS for Gross Anatomy – I and lecture noyes prepared by Dr.S.C.Dubal, College of Veterinary Sci & A.H., AAU. Anand (Gujarat) India

Biomechanics: Biomechanics and its application with reference to quadruped locomotion, kinetics of locomotion, stress and strain falling on locomotor apparatus, landmarks, angulation and weight bearing bones of ox, buffalo and comparison with other animals particularly horse and dog.

Contents:

Lecture – 1:

MECHANOBIOLOGYMechanobiology is the branch of biology which deals with the knowledge of

biomechanics incorporated with the knowledge of molecular biology, genomics and cellular biology. The mechanobiology has potential applications in cellular and tissue engineering. The body cells are constantly submitted to constraints (blood pressure, constraints linked to movement…). These vary from a few Pascals (shear constraints on the vessel wall) to MPas (constraints on the hip cartilage). These constraints are susceptible to influence the properties of the cell (physiology, synthesis, gene expression etc.) in the same way as biochemical modifications do. Thus, Mechanobiology is mainly concerned with the study of the influence of mechanical forces on cells and tissues and their clinical or therapeutical applications. Now biomechanics and biorheology are vigorous branches of mechanobiology. The micro and macro appropriate structural formations are therefore the result of cells influenced by functional stimuli followed by from selection. For example the nerve, muscle, gland cells by the related (electric)and chemical stimuli, bone cells and connective tissue cells by mechanical stimuli (e.g.,compression tension and shear etc. It is now possible to better understand the relation between local mechanical parameters and cellular functions (concept of mechanobiology). It is also reflected in as now known as Wolff law upon the adaptability of the bones which states that every change in the form and function of bone or of their functions alone is followed by certain definitive changes in their internal architecture and equally definitive secondary alterations in their external conformation in accordance with mathematical laws.

1. Biomechanics is the Newtonian mechanics to study the functional behavior of living organisms and reveals the effects caused by the constraints applied. The analysis and interpretations of the mechanical solutions are associated to understand the fundamentals structures and functions of the organisms.

2. Mechanotransduction 3. The transmission of a mechanical stimulus to a physiological phenomenon (ex:

secretion, expression of a receptor, activation of a gene…) arises in 4 major stages:i) Mechanical coupling which generally implies the transformation of the applied force into a force which is detectable by the cells or the induction of a physical phenomenon (e.g., pressure on a bone which induces a circulation of the fluid in the canalicular system and the appearance of a potential electrokinetic circulation). ii) Mechanotransduction which corresponds to the action of the forces exerted upon specific structures. Different hypotheses are today evoked and are the object of both mechanical and biological research (cytoskeleton which structures and orients itself, specific receptors in the areas which suffer high constraints, receptors linked to functional proteins (e.g., G-protein, ionic channels) and even, as has already been evoked, the existence of mechanosensitive receptors). iii) Signal transduction, i.e. the conversion of the mechanical signal into intracellular physiological signals.

BIOMECHANICS SYLLABUS for Gross Anatomy – I and lecture notes prepared by Dr.S.C.Dubal, College of Veterinary Sci & A.H., AAU. Anand (Gujarat) India

iv) Cellular response: regulation of a gene, release of autocrine or paracrine factors, expression of specific receptors… If stages 3 and 4 are usually clear for a number of cell types, the understanding of stages 1 and 2 demands the development of experimental models and approaches specific to each cell type studied (e.g., repartition of the constraints on and in the endothelial cell, polymerization and orientation of the cytoskeleton elements). Research in mechanobiology leads to medical and therapeutic applications in the vascular and cardiac in general and osteoarticular domains in particular. The incidence of the constraints is specific to a particular system and affects the physiology of the tissues: (1) by the production of extracellular matrix, e.g., cartilage), (2) by the production of specific secretions (e.g., production of NO, prostaglandins by the endothelial cells and blood circulation) and (3) by the induction by intercellular communication of specific functions.

4. With these new researches, mechanobiology is the promise of new diagnostic and therapeutic approaches. The most recent work shows that the incidence of mechanical forces is specific to the system under scrutiny and that stresses are implicated in tissue physiology (for example by the production of the extracellular matrix), secretions (i.e. production of NO and prostaglandins by endothelial cells), or for the induction of specific functions via intercellular communication; hence the interest from pharmacology in studies on new molecules. Moreover, these new findings have led to the development of tissue engineering, which is the concept of substitute tissue developed in vitro, from bioresorbable or non bioresorbable scaffolds and from cells harvested in a physiologic mechanical environment such as from cartilage, bone and vessels. At the same time, the problems of cell grafting in tissue repair and especially the use of stem cells have led to new therapeutic fields.

Lecture – 2:

LOCOMOTIONThe act of changing place or position by the entire body or by one or more of its parts

is called movement. Movement is one of the characteristic features of living organisms. Study of movements is called kinesiology.

In animals, movement is of two main types namely, muscular and non muscular. Muscular movements are further of two types namely, locomotion and movements of body parts. Locomotion is the movement of an animal as a whole from one place to another.Movements of body parts is that where an animal can move parts of its body.

The Basic Types of Movements Movement involves 3 basic mechanisms. They are amoeboid, ciliary and muscular.

Muscular movement is the method used in most of the vertebrates, including man. Muscular movement is based on the use of muscle fibres. Muscle fibres have the unique property of ability to contract and relax, which exerts a force. This force is responsible for movement of body parts and locomotion.

Quadruped movement and locomotion also result from co-operation between muscles and bones and joints. Hence study of LOCOMOTOR APPARATUS (Bones ,Joints and Muscles) and their Mechanobiological Properties in the animal body becomes essential.

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Lecture – 2:

LOCOMOTIONThe act of changing place or position by the entire body or by one or more of its parts

is called movement. Movement is one of the characteristic features of living organisms. Study of movements is called kinesiology.

In animals, movement is of two main types namely, muscular and non muscular. Muscular movements are further of two types namely, locomotion and movements of body parts. Locomotion is the movement of an animal as a whole from one place to another.Movements of body parts is that where an animal can move parts of its body.

The Basic Types of Movements Movement involves 3 basic mechanisms. They are amoeboid, ciliary and muscular.

Muscular movement is the method used in most of the vertebrates, including man. Muscular movement is based on the use of muscle fibres. Muscle fibres have the unique property of ability to contract and relax, which exerts a force. This force is responsible for movement of body parts and locomotion.

Quadruped movement and locomotion also result from co-operation between muscles and bones and joints. Hence study of LOCOMOTOR APPARATUS (Bones ,Joints and Muscles) and their Mechanobiological Properties in the animal body becomes essential.

ELEMENTARY BIOMECHANICS:1. Branches of Biomechanics:

a. Biostatics and Biodynamics (kinematics and kinetics)2. Definition of Displacement, Velocity, Acceleration, Force, Pressure, Work, Energy

and Power.3. Biomechanics of Deformity

(i) Stress (including types of stresses – compressive, tensile and shear stresses and stress concentration) and Strain and Moduli ( Young’s modulus of elasticity, shear modulus, bulk modulus and Poisson’ratio) and Bending

(ii) Elasticity and Plasticity(iii) Ultimate Load, Strength and Factor of safety.(iv) Biomechanics of Fracture/Rupture

INTRODUCTION

The movements of animals are controlled by a complex system of muscles and their tendons, bones and joints The study of locomotion requires solutions of a multiple approach of mechanics of multiple joint systems, hydrodynamics, aerodynamics and automated synchronizing controlling system. The muscles act as motor for power generation that is transmitted with help of their tendons to the bone and joint system. The bones act as links and the joints as kinks. They form kinematic chains. The totality of links so connected that if one of them is secured and another is set into motion, the remaining ones will of necessity move in a preset manner.

The task of engineering consists in constructing machines capable of executing definite movements. Veterinarians are often faced with the inverse problem to understand the mechanisms underlying the observed movements.

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DEFINITIONS:

Mechanics: It is a branch of science, which deals with the space, time and mass and establishes their relative relationships.

Biomechanics: It is that branch of mechanics, which concerned with the applications of laws of mechanics in understanding the mechanisms devised by living animals in general and locomotion in particular. It is divided in two principal branches:

A. Biostatics B. Biodynamics

BIOSTATICS

Biostatics: It that branch of biomechanics which deals with the conditions under which animal body (or part of its) remains at rest relative to their surroundings and the body is said to be in state of equilibrium. It is assumed that the body is acted upon by ` FORCES` which balance one another. The primary conceptions of biostatics are forces and the body upon which they act.

FORCES

Force: A force is that changes or tends to change the state of rest or uniform motion of body.

KIND OF FORCES

There are mainly three kinds of forces, viz.,1. Attraction or Repulsion2. Tension or Thrust3. Action and Reaction

1. Attraction and Repulsion: when one body on another body without any visible and physical means exerts a force, the force exerted is called the force of attraction (the bodied tend to approach each other) or repulsion (the bodies tend to separate from each other). In biostatics, the only force of this kind is therefore due to gravity (weight). The weight of a body is the force with which the earth attracts it towards its center. It is equal to mg (m = mass and g = gravitational acceleration).2. Tension: If a tendon (or a ligament) is tied to any point of a bone and if it tries to pull the bone at its other end. A force is exerted throughout the length of the tendon (ligament), which is called Tension or Pull.3. Thrust: If a animal push a body, it exerts some force on the body. Such a force is called Thrust or Push.

Important Properties:4. The tension of a light in extensible tendon (ligament) is the same

throughout its length along the tendon (ligament).5. If a weight is suspended from a light inextensible tendon (ligament), its

other end being tied to a fixed point, the tension remains the same throughout its length, and equals to the weight suspended

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6. When the tendon (ligament) is heavy, its tension varies from point to point on its length and depends upon the weight per unit length.

7. When two or more tendons (ligaments) are knotted together, the tensions are different in different portions on the two sides of the knot, though for each separate portion it continues to have a constant value.

8. If the tendon (ligament) is extensible, the tension will vary with the extension.

9. The Tension in a tendon (ligament) with a weight attached to one of its extremities, passing over a smooth surface like peg (sesamoid bones), pulley (trochlea), grooves etc., remains the same throughout its length and is equal to the weight suspended.

4. Action and reaction: When one body is in actual contact with another body, the force exerted at the point of contact by the first body on the second is called the Action b and the second on the first is called the Reaction. The two forces of action and reaction are equal in magnitude,opposite in direction and acts along the common normal at the point of contact of the bodies.

PRINCIPAL OF SUPERPOSITION AND TRANSMISSIBILITY OF FORCE:If a force F is acting at a point A on a rigid body, it is considered to be acting at any

other points (B, C, …) on the line of action of the force. The nature of force can vary from push to pull form or pull to push form (Fig.1). Thus, force is shifted from A to C through B. this is known as transmissibility of force. The Newton’s third law of motion asserts the principle of transmissibility of force. If several forces are simultaneously acting at the same point, the effect of all the forces is a algebraic sum of the forces. This is called as principle of superposition of forces. Each of the forces will produce the influence or effect as it would have produced while acting alone. That is the effect of different forces acting on a body is independent. This is called as principle of physical independence of forces.

F F F (-F) FA B C

Push Push Pull A B C Form Form Form

Fig. 1. Principle of Transmissibility of Force

BIODYNAMICS: It that branch of biomechanics which deals with the study of motion of a body or system of bodies, especially of forces that do not originate within the system itself. In order to describe the motion of a body or a point two things are required: (i) a frame of reference and (ii) a time-keeper It is not possible to describe absolute motion, but onlybmotion relative to surrounding objects; and a suitable frame of reference depends on the kind of motion that is desired to describe

The biodynamics is generally divided into two branches:1. Biokenematics: It concerns with the geometry of motion apart from all

conciderations of forces, mass or energy. The most suitable parameters are:(i) Displacement): It is the change of position.Thus displacement (s) = xf ─ xi, where xi, and xf are the intial and final positions of the body.Its scalar part is distance (d)

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(ii) Velocity (v): It is the rate of displacement i.e., the change of position per unittime.

v = (sf_─ si) / tf ─ ti = Δs / Δt = ds/dtIts scalar part is speed. (iii) Acceleration (a): It is the rate of velocity i.e., the change of velocity per unit

time.a = Δ v/ Δt = dv/dt = d2/dt2

Newton’s equation of motion:1. v = u + at, (1)2. s = ut + ½ at2 (2)3. v2 = u2 + 2 as (3)

where u = intial velocity and v = final velocity. (iv) Biokinetics: It concerns with the effects of forces on the motion of animal

bodies.The most suitable parameters are mass (m), momentum (mv), force (F), work (W) and energy (E).Newton’s laws of motion:

There are three laws of motion.1. First law of motion (Law of inertia): Every body perseveres ( remains) in its state of

rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces applied.

Mass (m): matter is one of primary conceptions of the mind, it cannot be defined satisfactorily. The property of matter that resists its state of motion is called as inertia and the measure of the inertia of a body is called its mass.Momentum (p): It is the product of mass of the body and its velocity. P = mv (4)

2 Second law of motion (measurement of force): The rate of momentum is directly proportional to the impressed force and takes place in the direction in which the force is applied

.F = dp/dt = d(mv)/dt = mdv/dt = ma (5)

Weight (W) is the gravitational force = mg

2. Third law of motion: For every action there is an equal and opposite reaction.

Pressure (P) : It is force exerting on per unit area.

P = F / A (6)Work (w) : It is the product of displacement and force in the direction of the displacement.

w = displacement × force in the direction of displacement (7)

= s Fcosθ

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Energy (E) : It is the measurement of ability of doing the work. Energy is of two types: 1. Potential energy (U): Energy possessed due to position of the body in a force

field. For example the potential energy in gravitational force of the Earth = mgh; H = height of the body from surface of the earth.2. Kinetic energy(T): Energy due to motion of the body.

T = ½ mv2

(8)

Power: The rate of change of energy is called as power.

P = E / t = ΔE / Δt = dE/dt = Fv(9)

Maximum stride speed of an animal (vmax) = (5 h P)1/3m −1/3)(10)

Where h = hip length; P = maximum power effort and m = mass of hind limb.

Figure 1. A tensile stress-strain curve

Definition and MeasurementStrain

In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. Strain is calculated by first assuming a change between two body states: the beginning state and the final state. Then the difference in placement of two points in this body in those two states expresses the numerical value of strain. Strain therefore expresses itself as a change in size and/or shape.

If strain is equal over all parts of a body, it is referred to as homogeneous strain; otherwise, it is inhomogeneous strain. In its most general form, the strain is a symmetric tensor.

The extension (ε) is positive if the material has gained length (in tension) and negative if it has reduced length (in compression). Because ε is always positive, the sign of the strain is always the same as the sign of the extension. Strain is a dimensionless quantity. It has no units of measure because in the formula the units of length "cancel out".

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Strain ε is defined in elementary form as the change in dimention (e.g., length) divided by the original dimention (e.g.,length).

ε = ΔL/L. (11)Stress Stress is a measure of force per unit area within a body. It is a body's internal distribution of force per area that reacts to external applied loads. There are three main stresses: 1. compressive stress (the applied force is compressive force), 2. tensile stress (the applied force is tensile (stretching) force and shear stress (the applied force is shear- the surface force that is parallel to the plane area). Stress is often broken down into its shear and normal components (compressive and tensile stresses) as these have unique physical significance. In short, stress is to force as strain is to elongation. Term normal stress has synonym in rheology (is the study of the flow of matter: mainly liquids but also soft solids or solids under conditions in which they flow rather than deform elastically)- extensional stress. Term normal stress has synonym in acoustics - longitudinal stress. Solids, liquids and gases have stress fields. Static fluids support normal stress (hydrostatic pressure) but will flow under shear stress. Moving viscous fluids can support shear stress (dynamic pressure). Solids can support both shear and normal stress, with ductile materials failing under shear and brittle materials failing under normal stress. All materials have temperature dependent variations in stress related properties, and non-newtonian materials have rate-dependent variations.

Yield Strength or Yield Point of a MaterialIt is defined in engineering and materials science as the stress at which a material begins

to plastically deform (Figure 1). Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible. In the three-dimensional space of the principal stresses (σ1,σ2,σ3), an infinite number of yield points form together a yield surface.

Knowledge of the yield point is vital when designing a component since it generally represents an upper limit to the load that can be applied. It is also important for the control of many materials production techniques such as forging, rolling, or pressing. In structural engineering, this is a soft failure mode which does not normally cause catastrophic failure unless it accelerates buckling.

It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding.

In physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress). Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.The linear elastic regime, strain is proportional to stress, but stress can be applied in more than one way (Figure 2). The tensile stress produces a proportional tensile strain :

E (12)

and the same is true in compression. The constant of proportionality, E, is called Young’s

modulus. Similarly, a shear stress s causes a proportional shear strain

Gs (13)

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http://en.wikipedia.org/wiki/Area


and a pressure p results in a proportional fractional volume change (or “dilatation”)

: Kp (14)

where G is the shear modulus and K the bulk modulus. All three of these moduli have the same dimensions as stress, that of force per unit area (N/m2 or Pa). It is convenient to use a larger unit, that of 109 Pa, Giga-Pascals, or GPa.

Young’s modulus, the shear modulus, and the bulk modulus are related, but to relate them we need one more quantity, Poisson’s ratio. When stretched in one direction, a material generally contracts in the other two directions. Poisson’s ratio, v, is the negative of the ratio of the lateral or transverse strain, ε, to the axial strain, , in tensile loading:

v = − εtrans / εlong (15)

Figure 2. (a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure.

Definition of Poisson's ratioPoisson's ratio v is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio. Poisson's ratio is usually represented as a lower case Greek v.

v = - εtrans / εlongitudinal

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Figure3: Poisson’s ratioWe might think that the way to measure the elastic modulus of a material would be to

apply a small stress (to be sure to remain in the linear-elastic region of the stress-strain curve), measure the strain, and divide one by the other. In reality, moduli measured as slopes of stress-strain curves are inaccurate, often by a factor of 2 or more, because of contributions to the strain from material creep or deflection of the test machine. Accurate moduli are measured dynamically: by exciting the natural vibrations of a beam or wire or by measuring the velocity of longitudinal or shear sound waves in the material.

Ultimate Load: The load (force) at which the material body ruptures or breaks or fractured is called as ultimate load (UL).Tensile strength (σs): It is ratio of ultimate load and the original cross-section area (A) of the material body.

σs = UL / A (16)

Working Load (WL): The force exerting on a body for doing the work.

Factor of safety: It is the ratio of working force and the ultimate load.

Factor of safety = WL / UL (17)

The factor of safety is the measure of design of safety margin of working load. It should always be more than one

Strength economy: It is the ultimate stress divided with density of material:Strength economy = Ultimate stress / Density (D) (18)

Stiffness economy: It the Young’s modulus of elasticity divided with density of material:

Stiffness economy = E / D (19)

BucklingIn engineering, buckling is a failure mode characterized by a sudden failure of a

structural member subjected to high compressive stresses, where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment, which does not form part of the primary forces to which the member is subjected.

Bending stiffness (BS) = It is the product of the Young’s modulus of elasticity (E) and the moment of inertia(I):

BS = E I (20)It is also called as flexural rigidity.

Slenderness ratio

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The ratio of the length of a column to the least radius of gyration of its cross section is called the slenderness ratio (sometimes expressed with the Greek letter lambda, λ). This ratio affords a means of classifying columns.

Slenderness ratio = Length (L) / Radius of gyration (ρ) (21)Radius of gyration (ρ): It is whole root square of ratio of moment of inertia to the area :

Ρ = [ Moment of inertia (I) / Area (A)]1/2 (22)

Torque (Т) = It is the moment of force which causes rotation in the material (e.g., bone):

T = GJθ / L (23)

Where G = Modulus of Shearing = E / {2(2 + v)} = E / {2(1 − 1/3)};L = Length;J = Centroidal polar moment of inertia of cross section Θ = Angle of twist and V = Poisson’ratio ( approx. = 1/3)

Shear Stress for twisted material:

Τ = T ρouter / J = G ρouter θ / J (24)

PlasticityIn physics and materials science, plasticity is a property of a material to undergo a

non-reversible change of shape in response to an applied force.Viscoelasticity

Viscoelasticity, also known as anelasticity, is the study of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material

Depending on the change of strain rate versus stress inside a material the viscosity can be categorized as having a linear, non-linear, or plastic response. When a material exhibits a linear response it is categorized as a Newtonian material. In this case the stress is linearly proportional to the strain rate. If the material exhibits a non-linear response to the strain rate, it is categorized as Non-Newtonian fluid. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. A material which exhibits this type of behavior is known as thixotropic. In addition, when the stress is independent of this strain rate, the material exhibits plastic deformation. Many viscoelastic materials exhibit rubber like behavior explained by the thermodynamic theory of polymer elasticity.Creep

Creep is the term used to describe the tendency of a material to move or to deform permanently to relieve stresses. Material deformation occurs as a result of long term exposure to levels of stress (physics) that are below the yield strength or ultimate strength of the material. Creep is more severe in materials that are subjected to heat for long periods and near melting

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point. Creep is often observed in glasses. Creep is a monotonically increasing function of temperature.The rate of this deformation is a function of the material properties, exposure time, exposure temperature and the applied load (stress). Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function — for example creep of a turbine blade will cause the blade to contact the casing, resulting in the failure of the blade. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures. Creep is not necessarily a failure mode, but is instead a deformation mechanism. Moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that otherwise may have led to cracking.

Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Creep deformation is "time-dependent" deformation.Fatigue

In materials science, is the progressive and localised structural damage that occurs when a material is subjected to cyclic loading. The maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material.The process starts with dislocation movements, eventually forming persistent slip bands that nucleate short cracks. Fatigue is a stochastic process, often showing considerable scatter even in controlled environments. The greater the applied stress, the shorter the life. Fatigue life scatter tends to increase for longer fatigue lives. Damage is cumulative. Materials do not recover when rested. Fatigue life is influenced by a variety of factors, such as temperature, surface finish, presence of oxidizing or inert chemicals, residual stresses, contact (fretting), etc.Fracture

Fracture is the (local) separation of a body into two, or more, pieces under the action of stress. The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal. Sometimes, in crystalline materials, individual crystals fracture without the body actually separating into two or more pieces. Depending on the substance which is fractured, a fracture reduces strength (most substances) or inhibits transmission of light (optical crystals).Types of fracture

In brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension.

In ductile fracture, extensive plastic deformation takes place before fracture. Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain before fracture under favorable loading condition and environmental condition. The strain at which the fracture happens is controlled by the purity of the materials. At room temperature, pure iron can undergo deformation up to 100% strain before breaking, while cast iron or high-carbon steels can barely sustain 3% of strain. Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modeled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation before the crack actually propagates. The basic steps of ductile fracture are necking (which results in stress localization at the point on the sample of smallest cross-sectional area), void formation, void coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface.

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http://en.wikipedia.org/wiki/Metal

http://en.wikipedia.org/wiki/Bone


Biomechanics of rupture of tendon:The ultimate load when expressed in terms of unit area is known as tensile strength.

Theoretical value of TS should about 0.1 E. However, the observed TS is always several times less. This discrepancy is due to the presence of micro-cracks which reduces the strength. The factors responsible for micro-damage of equine tendons are cross-sectional area and collagen content, composition of extra-cellular matrix), longitudinal heterogenecity, inter-fibre differences and elevation of core temperature.

There is initially a tiny internal void, which grows into a micro –crack in tensile strain. Further formation of a crack relieves the elastic stress. As long as the length of the micro-crack remains below a certain value, energy is required for it to develop. Further extension of tendon results in a reduction of its energy. Thus, a rise in temperature will enhance the progress of micro-crack. The cyclic tensile loading of equine tendon has been shown to result in an elevation of core temperature. The cyclic overloading creates cumulative micro-damage. When the transverse length of this micro-damage reaches a critical value (say critical length of destructive process or simply critical length of micro-damage), there is spontaneous rupture of the material. An increase in tensile strength decreases in the plastic work done in initiating fracture at the tip of flaws.

Figure 4: Relation between energy of propagation of micro-crack and transverse length of micro-crack

The rate of growth of micro-crack is related with a measurement known as stress concentration factor (K). It describes the distribution of stresses at the crack tip. When the value of K achieves a critical value, it is known as fracture toughness, there is catastrophic failure of the material. The extensor tendons of fore limb, the gastrocnemius tendon and Achilles tendon had high tensile strength. Hence, these tendons appeared to be highly susceptible to develop flaws.

A low but repeated (continuous or intermittent) stress can cause the rupture of the tendon. This minimum stress is known as fatigue tensile stress, which is obtained by stress-strain (SN) curve.

From clinical point of view, the critical length of micro-damage and the number of cycles of fatigue failure are important.

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The critical length of micro-damage indicates the maximum transverse damage, which a tendon can sustain under tensile strain. When the tendon attains the critical length, it ruptures under the applied stress. The higher the stress the less is the durability of the tendon.

Tensile strength (TS) of a tendon is obtained by dividing the UL with its original CSA. Factor of safety (FS) is obtained by dividing the UL with the WL. The critical length (CL) of destructive process (the transverse length of micro-damage) is calculated as follows:

CL = 2 G E / (TS) 2, (14) G = Surface free energy of the tendon per unit area

The exact value of G is not known. The most probable value of G is assumed to be 0.50 10 3 J / m2.

The fracture toughness (FT) was calculated as follows:

FT = (TS) ( CL)½

= (2 G E) ½ (15)The fatigue tensile strength (FTS) of a tendon is obtained by its minimum WL (assumed to be equal to 4 CSA of its belly.

The number of cycles (N) of repeated loading that could produce the failure is calculated as follows:

d(CL)/dN = C ( FTS ) n ( CL ) n/2 (16) C = Constant.

Since CL<< diameter of the tendon, then for n = 2, from eq (3) we get,

N = (CL) / C ( FTS ) 2 (17)

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LECTURE - 3

MECHANOBIOLOGY OF HISTOGENESIS:1. Fibrous tissues 2. Cartilage and 3. Bone

Biomechanics of Bones under: 1. Compression or Tension ( biomechanics of Vertebrae)2. Bending in One Plane ( I-Beam – Mandible, Zygomatic arch, Ilium and Neural

spines)3. Bending in MultiPlanes ( Column – Long bones of appendages)

LECTURE - 4

BIOMECHANICS OF SKELETAL MUSCLES1. Force generated by a skeletal muscle2. Types of Muscles ( Parallel fibred and Pinnated muscles)3. Endurance and Strength of Muscle (fibre types and per cent population) in relation to

draught ability of the animal

LECTURE - 5

BIOMECHANICS OF MOTION1. Centre of Gravity 2. Force and Lever Arm System (Bone – Joint – Muscle System as Machine and relating

it with size of head and neck and body trunk)3. Velocity and Lever Arm system4. Muscle Mechanics (The Most for the Least)5. Stay Apparatus

LECTURE – 6

GAIT1. Definition2. Gait characteristics (stride, stride length, stride frequency, stride speed3. Animal classified on the basis of Foot Posture (Plantigrade, Digitigrade and

Unguligrade)

4. Maximum Speed of Running (Umax) = (5hP)1/3 / m 1/3

Where h = Hip length; P = the Maximum Power Generated by the animal for the motion and m = Mass of the Hind limb (Dubal, 1997: Ph. D. Thesis submitted to Gujarat Agricultural University, Dantivada, Banaskantha, Gujarat, India)

LECTURE – 7

MECHANOBIOLOGY OF SYNOVIAL JOINT LUBRICATION

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1. Histology of Articular Cartilage (AC) emphasizing the space orientation of fibres and cells

2. Biochemistry of AC3. Biomechanical Properties of AC4. Mechanobiology of AC5. Theory of Synovial Joint Lubrication

The lectures should incorporate the clinical applications pertaining to the topic.

Practical: Biomechanics and kinetics of locomotion.

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Biomechanics Lecture Notes

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