5103.TissueMechanics (2)

8/3/2019 5103.TissueMechanics (2)

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Monday, Jan. 9,2012 Define

Stress, strain, tension, compression, shear Describe loading patterns

Bending loads

Describe force-elongation curve(structural properties)

Describe stress-strain curve (materialproperties) Stiffness, failure

Understand material properties of: Anterior cruciate ligament

Understand muscle length-tension

curve

Types of Forces

Tension

Tensile force or stress

Example - Tensile Forces

Patellar tendon rupture


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Compression

Axial stress

Results fromforces directedtoward each other

Compression - Example

Vertebral Fracture

Example - CompressionDisc Problem Types of Force/Stress

Tension

Compression

Shear


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Shear Force - Examples Combined Loads

Create shear +/- compression +/-tension

Torsion (twisting)

Bending

Most common way forces areapplied in/to the body

TorsionTorsion - Example

Tacoma Narrows Bridge

Twisted and fell into Puget Sound

November 7, 1940


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Torsion - example

Tibial Spiral Fractures 19 y.o. male

basketball player

Ran & jumped toblock a shot

Felt pop andpain

Carl et al., THE PHYSICIAN AND SPORTSMEDICINE - VOL 25 - NO. 6 - JUNE 97

Torsion - Example

Ankle Fracture 26 y.o. male hockey player. Caught foot,

twisted and fell

Bending LoadsBending Loads


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Stress - Bending & Axial

Axial = compression

Bending Forces - Neck of

Femur

Bending Forces - ExampleStress Fracture of Neck of

Femur

Compression + tension - ExampleSuspension Bridge


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Force & deformation Strain

Change in length

the ratio ofelongation withrespect to theoriginal length,

Strain vs Deformation

Deformation = elongation of tissuewhen force is applied

Strain = change in length relative tooriginal length

E = l - lolo

In Vivo Strain

Difficult tomeasure

Requires gaugeon tissue


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Force & deformation

Elastic

Deformation islinearly related toforce

Force vs Stress

Force (N) is absolute value of forcerequired to produce tissuedeformation

Stress is force divided by cross-sectional area

Force & stress

Force = P

Stress = F/A = N/m2

= F/A

1 Pascal (Pa) = 1 N/m2

1 megapascal (MPa)= 106N/m2

Stress - Bending & Axial

Axial = compression


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Structural vs Mechanical

Properties

Structural Properties

Related to size, or

Related to length

Material Properties

Independent ofsize

Eg. Calculating Stress &

ForceFor example: The force needed to break a piece of steelwire with a cross sectional area of 2x106 m2 is 2400 N.What is its breaking stress?

What force would be needed to break a steel bar with across section of 5x104m2?


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Eg. Calculating Stress &

ForceThe breaking stress= breaking force area= 2400 2x106= 1,200,000,000 Nm2= 1.2 GpaTo break the steel bar, the force needed= breaking stress x area= 1.2x109 x 5x104= 600,000 N

Stress - Elastic

Stress linearlyrelated to strain

Implies materialdeformsproportional tostress

Material returnsto original shapeif load removed

Stiffness

Slope of stress-strain curve

Higher number =stiffer material

Plastic Behaviour

Yield point =elastic limit

After yield point,material deformsmore, and doesnot return tooriginal shapewhen load isremoved


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Mechanical Strength

Yield strength =permanent change inmaterial

Ultimate strength =maximum load

Failure strength =load wheredisruption occurs(rupture strength)

Failure strain =strain when failureoccurs

Strength of various

biological tissues Tendon 45 -125 MPa (100 N/mm2)

ACL sutures - 250 - 400 N

ACL = 350 - 2000 N

Bone 100-150 Mpa

Shoulder ligaments 4-6 MPa

Examples

Stiffness = slopeof stress-strain

curve


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Example - Spider Silk

Stress-Relaxation

Apply a stretch(deformation) -

hold Tissue will relax

over time - lessload required tomaintaindeformation

Creep

Apply a load

Tissue will

elongate overtime (creep)


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Fibers are stretched in thelinear region

- 5-6% elongation

Some fibrils rupture

(microfailure)

Mechanism of Tendon Injury

Wavy fibers

straighten

AnteriorCruciateLigament

ACL Reconstruction With Autografts

Weighing Performance Considerations and Postoperative Care

John A. Grant, PhD; Nicholas G. Mohtadi, MD, MSc

THE PHYSICIAN AND SPORTSMEDICINE - VOL 31 - NO. 4 - APRIL

2003

Testing the ACL - How

Mechanical testing system


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Testing the ACL - resultsACL - Effects of

Immobilization

ACL Grafts

Takes approximately 3 years toremodel

Weakest for 3 mo. after surgery

Patellar tendon graft most stable inlong-term, but

Hamstrings graft stronger initially


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Tendon Forces - Combined

Abnormal forces -

Example Alignment may

cause increase in

strain (& stress) Correct by using

shoe insert

Patellofemoral Stress

Degrees Area (cm2) Force Stress

20 2.6 238 0.92

30 3.1 615 ??

50 3.9 ?? 7.0090 ?? 4186 10.21

Huberti,HH; Hayes,WC [1984]): Patellofemoral contact pressures: the influence of

Q-angle and tendofemoral contact. J. Bone Joint Surg. 66-A(5), 715-724.)

Escamilla,RF (2001): Knee biomechanics of the dynamic squat exercise.

Med. Sci. Sport. Exercise. 33(1, Jan), 127-141.

?? = you calculate; Stress = Force/Area


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Muscle length-tension relationship Muscle length-tension relationship


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5103.TissueMechanics (2)

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