From last time

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From last time

• Biomechanical Concepts
• Kinematics
• Kinetics

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Biomechanical ConceptsFluid Mechanics, Joint
Motion, Leverage, Stress and Strain

• ESS 5310-001
• Lecture 4
• Reading WZ Chapter 3

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Overview

• Fluid and Joint Mechanics
• Joint Motion
• Leverage
• Deformation Applied Forces
• Normal and Shear Stress Strain
• Material Properties
• Stress Strain
• Elastic, Plastic and Viscoelastic Behavior
• Creep Relaxation Responses
• Strain Energy Material Properties
• Fatigue Testing

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Part 1

• Fluid Mechanics

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Fluid Resistance

• Fluids
• Gas (e.g., air)
• Liquid (e.g., water)
• Fluids resist the movement of objects through
  them
• Determining the magnitude and direction of fluid
  resistance is very complex

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Fluid Properties

• Fluid properties which influence resistance
• Density
• Mass per unit volume
• Increase density, increase resistance
• Air density is affected by humidity, temperature,
  and pressure
• Viscosity
• Fluids resistance to flow
• Air viscosity increases with air temperature

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Fluid Resistance

• Object disturbs fluid
• Disturbance is dependent upon density and
  viscosity of fluid
• Increased disturbance correlates with increased
  energy passing from the object to the fluid
• Transfer of energy is termed fluid resistance
• 2 components of fluid resistance are drag and lift

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Drag Force Component

• Fdrag drag force (fluid resistance)
• Cd coefficient of drag (an index of how smooth
  and streamlined the object is)
• A projected frontal area of object (area facing
  flow)
• ? fluid viscosity
• v relative velocity (velocity of object
  relative to fluid)

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Drag (Force) Component
Surface Drag - Boundary layer (contact with
fluid) - Surface area Viscous Drag - Fluid
viscosity
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Fluid Flow

• Laminar Flow
• Small smooth object
• Small velocity
• Separated Flow
• Turbulent Flow
• Fluid is unable to contour to object shape
• Fluid separates as it passes object
• Turbulence forms behind object

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Lift (Force) Component
So, an object will tend to travel (lift) in the
direction of least pressure
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Bernoullis Principle
Air has to travel further over the top of the
airfoil, hence greater air velocity and less air
pressure in that region.
Go to the lightthe light is good
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Magnus Effect (Force)
Follow the path of least resistance
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Part 1 Summary

• Fluid Properties
• Density
• Viscosity
• Fluid Resistance
• Drag
• Flow
• Lift
• Bernoulis Principle
• Magnus Force

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Part 2

• Joint Motion

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Joint Motion

• Reference Positions
• Planes and Axes
• Relative Position
• Joint Motions

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Reference Positions

• Anatomical Position
• Standard reference point
• Palms face front
• Fundamental Position
• Similar to anatomical position
• Arms more relaxed
• Palms face inward

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Relative Position

• Medial toward midline of the body
• Lateral away from midline of the body
• Proximal toward point of attachment
• Distal away from point of attachment
• Superior toward the top of the head
• Inferior toward the bottom of the feet

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Relative Position

• Anterior front, ventral
• Posterior back, dorsal
• Ipsilateral on the same side
• Contralateral on opposite sides

• Relative angle
• - Included angle between two segments

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Relative Position
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Planes Axes

• Plane
• Flat, two-dimensional surface
• Cardinal Planes
• Planes positioned at right angles and
  intersecting the center of mass
• Divide body into perfect halves
• Axis of Rotation
• Point about which movement occurs
• Perpendicular to plane of motion

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Cardinal Planes

• Sagittal Plane
• Left Right halves
• Medio-lateral axis (frontal)
• Frontal (Coronal)
• Front Back halves
• Antero-posterior axis (sagittal)
• Transverse (Horizontal)
• Upper Lower halves
• Longitudinal axis (transverse)
• Many other planes exist

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Joint Motions, Planes Axes

• Sagittal Plane and Medio-Lateral Axis
• Joint Motions
• Flexion
• Extension
• Frontal Plane and Anterior-Posterior Axis
• Joint Motions
• Abduction
• Adduction
• Transverse Plane and Longitudinal Axis
• Joint Motions
• Internal Rotation
• External Rotation
• Rotation (left and right for head and trunk)

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Table 3.1
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Joint Mobility versus Stability

• Joint Mobility
• Measured through ROM or functional ROM
• Joint Stability
• Ability of a joint to maintain functional
  position throughout its ROM
• Ability of a joint to resist dislocation

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Factors Influencing Joint Mobility

• Shape of articular surfaces making up joint
• Boney structures or surfaces
• Passive Restraints
• Ligaments, joint capsule, cartilage
• Active Restraints
• Muscle Action
• Injury
• Occurs when allowed or normal ROM is exceeded

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Table 3.2
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Joint Mobility and Stability

• Relatively immobile
• Limited ROM
• Tight boney fit
• Numerous ligaments
• Support structures
• Large muscle group

• Unstable
• Large ROM
• Loose boney fit
• Limited extrinsic support
• Minimal surrounding muscles

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Part 2 Summary

• Planes and Axes
• Absolute and Relative Position
• Joint Motion
• Joint Mobility and Stability

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Part 3

• Leverage

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So whats a lever?

• A bar turning on a fulcrum to lift or move
  weights
• Webster
• Think of
• The bar as our skeleton (limb segments)
• The fulcrum as some joint
• The weights as our limb weight or other
  resistance or load
• The force arm as the moment arm of the muscle
• The resistance arm as the moment arm of the load

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Purposes of Levers

• Increase affect of applied force
• Different moment arms
• Increase effective speed (velocity) of movement
• Figure 3-20

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Rotation Leverage

• All lever systems contain
• Effort Force (F)
• Applied force
• Resistive Force (R)
• Load, resistance
• Axis of Rotation (A)
• Fulcrum

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Mechanical Advantage (MA)

• where MA is Mechanical Advantage
• If MA gt 1, the lever favors strength (effort)
• If MA lt 1, the lever favors speed
• If MA 1, the lever favors neither

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Lever ClassificationRemember ARF 123

• 1st Class (Axis is in the middle)
• MA varies (strength or speed)
• Dependent on placement of resistance and force
  relative to axis
• 2nd Class (Resistance is in the middle)
• Favors effort force (strength)
• MA gt 1
• A smaller effort force can balance a larger
  resistive force
• 3rd Class (Force is in the middle)
• Favors range (ROM) and speed of movement
• MA lt 1

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Leverage
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Moment of Force

• Line of force action actually changes through ROM
• Affects moment arm
• Irregular joint structure
• Not true pin joints
• Changes in muscle force and moment arm through
  ROM dictate continuously changing moment
• Plus magnitude of muscle force varies
• Muscle length
• Contraction velocity
• Level of neural activation
• Level of fatigue

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Joint Reaction Forces

• Net effect of muscle forces and other forces
  (usually due to position) acting across joint
• Utilize models to estimate forces occurring
  across joints
• Bone on Bone Forces
• Include joint forces created by passive
  structures
• Synovial Fluid
• Lubricant, shock absorption, nutritional
  functions
• Reduces friction and improves durability

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Part 3 Summary

• Leverage
• Mechanical Advantage
• Lever Classification
• Joint Reaction Forces

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Part 4

• Deformation, Stress Strain

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Deformation

• The magnitude of change in an objects shape in
  response to the application of external forces or
  moments.
• Factors Influencing Deformation
• Material properties
• Size and Shape
• Environmental Factors (e.g. temperature,
  humidity)
• Magnitude, Direction and Duration of the Applied
  Force

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Deformation

• Characteristics of deformation my indicate the
  type of applied mechanical force or load
• Elongation Tension
• Shrinkage Compression

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Applied Forces

• Axial Forces
• Act perpendicular to the area on which they act
• e.g. compression, tension
• Tangential Forces
• Act parallel to the surface area on which they
  act
• e.g. shear
• Objects also deform as a result of bending or
  torsion

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Applied Force and Deformation

• Tissue may respond differently to different load
  configurations
• A tissue may stretch a greater magnitude from a
  500N tensile force than it shortens from a 500N
  compressive force.
• A tissue may respond differently when the tensile
  force is preceded by a compressive force,
  compared with a tensile force alone.

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Normal and Shear Stress

• Stress
• Applied (distributed) load or force (internal or
  external) over an area or surface of material or
  tissue
• Units N/m2 or Pascal
• Normal Stress (s, sigma)
• Stress is applied perpendicular to the surface or
  area
• Assume force is distributed uniformly over the
  area
• s F/A force/area
• Shear Stress (t, tau)
• Stress is applied tangent to the surface or area
• Assume force is distributed uniformly
• t F/A force/area

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Normal versus Shear Strain

• Strain
• Measure of the degree of deformation
• Units of length / length, thus unit-less or in
• Normal Strain (e, epsilon)
• Ratio of change in length to the original length
• e ?l / l change in length / original length
• If the length decreases, then compression
• If the length increases, then tension
• Shear Strain (?, gamma)
• Refer to figure
• Shear strain d/h, or tan ? d/h
• ? is usually small, thus ? angle ? in rad
• Average shear strain ? d/h

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Stress-Strain Diagrams

• O - Origin
• P Limit of proportionality
• E Elastic limit
• Y Yield point
• sy is yield strength of material
• Substantial elongation can occur without an
  increase in load
• U Highest stress point
• su is ultimate strength of material
• Substantial elongation can occur without an
  increase in load
• R Rupture or fail point

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Stress-Strain The Curve
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Elastic and Plastic Deformation

• Elastic Response
• Deformation in response to loading
• Load removed
• Returns to original shape/length
• Plastic Response
• Microtears debonding of fibers
• Load removed
• Permanently deformed
• Damaged

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Elastic Behavior

• For linear elastic materials
• The slope (k) is an estimate of the materials
  elastic modulus is a straight line

k s / e
s
e
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Measures of Elasticity

• Elastic Modulus (k)
• Stiffness of a material
• k stress / strain
• k s / e
• For Linearly elastic materials
• s Ee
• Modulus of Elasticity (E)
• Youngs Modulus
• Slope of Stress-Strain Curve
• Residual Strain
• Difference between original length and length
  resulting from stress into the plastic region

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Plastic Behavior

• Portion between yield and failure
• Material does not return to original length when
  stress is removed
• Damage

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Viscoelasticity

• Exhibit gradual deformation and recovery when
  subjects to loading and unloading
• Response is dependent upon how quickly the load
  is applied or removed.
• Extent of deformation is dependent on the rate of
  loading
• Stress-strain relation (curve) is a function of
  time or rate at which the stress is applied
• Thus, having both fluid (viscosity) and material
  (elasticity) properties and responses to loading

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Types of Material

• Elastic
• Linear relationship between stress and strain
  (springs back)
• Viscoelastic
• Non-linear relationship between stress and strain
• springs back eventually
• Hysteresis
• Represents energy lost in a viscoelastic material
  during release/return

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Energy

• Elastic Materials
• Energy to deform is stored as strain energy
  (potential energy)
• Available to help return material to its original
  shape when load is removed
• No energy is lost
• Elasto-plastic Materials
• Some of the strain energy is returned
• Some of the strain energy is dissipated as heat
  in high stress conditions
• Viscoelastic Materials
• Some of the strain energy is stored as potential
  energy
• Some is dissipated as heat regardless of stress
  levels

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Stored Mechanical Energy

• Proportional to area under stress-strain curve
• ME ½ s e
• Spring, rubber band, trampoline

Mechanical Energy
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Viscoelastic MaterialsForce-Deformation Curve
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Part 4 Summary

• Deformation
• Applied Forces
• Stress-Strain Curve
• Material Properties
• Elasticity
• Plasticity
• Viscoelasticity
• Mechanical (Strain) Energy

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Part 5

• Loading Material Properties

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Loading

• Uni-Axial Loading
• Compression
• Tension
• Pure Shear
• Multi-Axial Loading
• Torsion
• Typical Shear
• Bending

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Uni-Axial Loading
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Multi-Axial Loading
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ViscoelasticityCreep
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ViscoelasticityStress Relaxation

• Strain is held constant
• Amount of stress required to maintain strain
  progressively decreases

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Material Properties of Tissues

• Anisotropic - Direction Specific
• Response is dependent on direction of load
  application
• Viscoelastic - Time Dependent
• Response is dependent on rate duration of
  loading

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Stress StrainMaterial Strength
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Stiffness

• Slope of the load deformation curve
• Youngs Modulus
• e.g. Bone is flexible and weak

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Material Strength Mechanical Failure

• Failure Strain
• Strain exhibited when failure occurs
• Ductile versus Brittle materials
• Toughness
• Measure of the capacity to sustain permanent
  deformation
• Total area under the stress-strain diagram
  (larger area tougher)
• Resilience
• Ability of a material to store or absorb energy
  without permanent deformation
• Measured by modulus or resilience (area under the
  elastic region of the stress-strain curve)
• Elastic Strain Energy

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Material Characteristic Properties

• Ductile
• Exhibits a large plastic deformation prior to
  failure
• Brittle
• Shows sudden failure (rupture) without undergoing
  much plastic deformation
• Homogeneous
• properties do not vary from location to location
  within the material
• Isotropic
• Properties are independent of direction of
  loading
• Incompressible
• Material has a constant density

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Strength of Material

• Failure point or load sustained before failure
• Failure can be caused by
• Single traumatic event
• Accumulation of microfractures
• Strength is assessed by
• Energy storage
• Area under stress-strain curve

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Fatigue and Endurance

• Loads that may not cause failure in a single
  application, may cause failure if applied
  repeatedly.
• Fracture that results from repeated loading, is
  called Fatigue

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Fatigue Testing

• Cyclical Loading
• N is number of repetitions
• s is the load (stress)
• A Loading of specimen
• B Loading Cycle
• C Fatigue Response
• Corresponding s is the relative fatigue strength
  for that number of cycles

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Fatigue Behavior

• Factors influencing Fatigue Behavior
• Temperature
• Higher temps, lower fatigue strength
• Surface imperfections and discontinuities
• Result in increased fracture propagation and
  hence ultimate failure rupture earlier in cycle

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So why is it important to know these properties?

• What can we do with the knowledge?

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Modeling

• Types of Models
• Physical (crash test dummies)
• Mathematical (equations to mimic real impacts)
• Advantages?
• Disadvantages?

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Part 5 Summary

• Loading
• Material Properties
• Stiffness
• Strength
• Endurance
• Fatigue
• Modeling

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For next time

• Work on Problem Set 2
• Due next week let me know if you need more time
• Feel free to work together
• Next week
• Start into Chapter 4
• Tissue Biomechanics and Bone