principles of Biomechanics

definitions

Biomechanics

· science of action of forces on bondy

Statics

· study of action of forces at rest

Dynamics

· study of action of forces that produce motion

· kinematics

· study of motion in terms of displacement, velocity and acceleration

· kinetics

· study of action of forces and their resulting action

· kinesiology

· study of human movement

Force

· push or pull causing

· external effects (acceleration)

· internal effects (strain)

· forces split into components

· Fx = F cos 0

· Fy = F sin 0

· resultant force

· single force equivalent to system of forces acting on body

Moment

· rotational effect of force on a body about a point

· any force acting at a distance from a point can produce a moment

· moment arm is perpendicular distance from force to axis of rotation

· moment (or torque) = force x length of moment arm

Free body diagram

· sketch of body or part showing all forces acting on it

· weight of object acts through centre of gravity

· centre of gravity for body is just anterior to S2

Work

· force acts on body to cause displacement

· work = force x displacement

Energy

· ability to perform work

· energy is conserved

· two types

· potential energy

· stored energy

· ability of body to perform work as a result of its position or configuration

· kinetic energy

· energy of body due to its motion (velocity)

Moment of inertia

· quantity that takes into account

· cross-sectional area

· distribution of material around neutral axis

1. Area moment of inertia

· reflects bending rigidity

· formula for rectangle is base x height³ / 12

· bending rigidity also proportional to length

2. Polar moment of inertia

· reflects torsional rigidity

· formula for cylinder is radius⁴

forces

Tension

· equal and opposite loads outward from surface

· tensile stresses produced

· maximal tensile stress on plane perpendicular to load

· structure lengthens and narrows

Compression

· equal and opposite loads toward surface

· compressive stresses produced

· maximal compressive stress on plane perpendicular to load

· structure shortens and widens

Shear

· load applied parallel to surface

· shear stresses produced

· structure deforms internally in an angular manner

· tensile or compressive forces produce shear stresses

Bending

· loads applied to cause bending about an axis

· combination of tension and compression

· tensile stresses on one side

· compressive stresses on other side

· neither along neutral axis

· magnitude of stress proportional to distance from neutral axis

· bending may be produced by

· three forces (two one way and middle one the other)

· four forces (two force couples at either end)

· failure occurs at

· middle force (three forces)

· between force couple (four forces)

Torsion

· load applied to cause twisting about an axis

· torque or moment produced within structure

· shear stresses produced

· magnitude of stresses proportional to distance from neutral axis

· maximal shear stresses produced on planes parallel and perpendicular to neutral axis

· maximal tensile and compressive stresses produced on plane diagonal to neutral axis

structural and material properties

Structural

· related to

· material that object made of

· geometry of object

· when load applied to object, it undergoes deformation

Load-deformation curve

· initially constant increase (straight line)

· represents elastic zone

· material returns to original shape when load removed

· slope of line reflects rigidity of object

· extends to yield point

· yield point reflects elastic limit

· then line flattens off (curve)

· represents plastic zone

· material does not return to original shape when load removed

· extends to ultimate point

· failure occurs at this point

· area under curve represents energy absorbed by object

· also represents strength of object

· load-deformation curve useful to determine mechanical properties of whole structures

Material

· independent of geometry of object

Stress

· represents intensity of internal force

· stress replaces load of structural properties

· stress = force per unit area

· units of N/m or pascals (Pa)

· may be perpendicular to surface

· tensile or compressive stress

· may be parallel to surface

· shear stress

Strain

· relative measure of deformation

· strain replaces deformation of structural properties

· strain = change in length / original length

· no units (percentage)

Stress-strain curve

· similar to load-deformation curve

· similar

· elastic zone and yield point

· plastic zone and ultimate point

· energy under curve

· stiffness of material represented by slope of curve

· (Young’s) modulus of elasticity = stress / strain in elastic zone

· hysteresis

· different shape of curve between application and removal of load

· represents absorption of energy by material

· stress-strain curve useful to determine mechanical properties of material (cf. whole structure)

Properties of materials

Brittle

· linear stress-strain curve to ultimate point

· no deformity then sudden failure

Ductile

· large curved region to ultimate point

· large amount of deformation before failure

Viscoelastic

· time-dependent stress-strain behaviour

Isotropic

· have the same mechanical properties in all directions

Anisotropic

· mechanical properties vary with direction of loading

Homogeneous

· uniform structure and properties throughout

Concepts

Creep

· property of viscoelastic material

· occurs when object subjected to action of constant stress

· rapid increase in strain

· then gradually increasing strain to equilibrium point

Stress relaxation

· property of viscoelastic material

· occurs when object subjected to constant strain

· rapid increase in stress

· gradual decrease in stress to equilibrium point

Fatigue

· failure produced by

· single load that exceeds ultimate strength

· repeated loads of lower magnitude

· failure from repeated loads is fatigue failure

· produced by

· few repetitions of high load

· many repetitions of lower load

· failure according to load and repetitions can be plotted as fatigue curve

· is asymptotic

· below certain load, failure will never occur

metals

Corrosion

· release of ions and compounds as a result of chemical action

Uniform

· corrosion of surface of metal

Galvanic

· when two different metals placed in contact in electrolyte

· electrons move from base to noble metal

· base metal becomes anodic and more susceptible to corrosion

· noble metal becomes cathodic and more resistant to corrosion

Stress

· tensile side of metal is anodic and prone to corrosion

Crevice

· surface defect in form of crevice or crack leads to relative oxygen depletion

· defect becomes anodic and corrosion facilitated

Pitting

· surface defect in form of pit or impurity leads to similar anodic degradation

Fretting

· abrasive wear accompanied by corrosion

· protective oxide layer removed by abrasion and corrosion can occur

friction

· resistance to movement of two bodies in contact

Types

· two types

Surface friction

· due to

· adhesion of surfaces due to roughness

· viscosity of lubricant

· friction directly proportional to applied load

· friction not related to area of contact

· variable is coefficient of friction

· friction = coefficient of friction x load

Bulk friction

· from internal energy dissipation mechanisms within bulk material or within lubricant

· example is in articular cartilage

· internal friction caused by viscous drag when fluid flows through matrix

Lubrication

· attempt to reduce coefficient of friction

· dependent on

· surfaces

· lubricant

· velocity

· two types of lubrication

Boundary lubrication

· boundary lubrication is single monolayer of lubricant molecules adsorbed onto each bearing surface

· independent of

· physical properties of lubricant (eg. viscosity)

· physical properties of surface (eg. stiffness)

· depends on chemical properties of lubricant

Fluid film lubrication

· fluid film lubrication is thin fluid film separating surfaces

· film causes greater bearing surface separation

· load supported by pressure in fluid film

· two types

· hydrodynamic

· nonparallel rigid surfaces slide on each other

· form converging wedge of fluid

· squeeze film

· rigid surfaces approach each other

· fluid squeezed out

· in both, characteristics dependent only on physical properties of lubricant

· different form of lubrication occurs with deformable surfaces

· called elastohydrodynamic lubrication

· pressure in fluid deforms surfaces

· surface area increased

· lubricant escapes less readily

· longer lasting film generated

· lower stress of articulation

· weeping lubrication

· at least one of surfaces porous

· elastohydrodynamic lubrication augmented by fluid expressed from deforming surface

· forms pressurised lubricating mechanism

WEAr

· wear is removal of material from solid surfaces by mechanical action

Interfacial wear

· occurs when bearing surfaces come into direct contact with no lubricant separating them

· two types of wear

· adhesive wear

· surface fragments adhere to each other

· torn from surface during sliding

· abrasive wear

· soft material scraped by harder one

· harder material can be opposing bearing or loose particles

Fatigue wear

· due to accumulation of microscopic damage within bearing material under repetitive stressing

· can occur in well-lubricated bearings