Lecture 2
Objectives:
1.
2.
Continue with concepts of Stress/Strain and Load/Deformation
Biomechanics of bone and articular cartilage
Properties of Connective Tissues
Stress/Strain
Stress = Force/Area (N/cm2, N/m2(pascals), MN/m2 (Mpascals))
Stress = Load
Strain =
Length / Original Length (percentage change)
Strain = deformation
Types of Stress:

Tensile (distractive) – 2 externally applied forces that are equal and act along the same line in
opposite directions = tensile force/cross-sectional area

Compresssive – 2 externally applied forces that are equal and act along the same line toward each
other on opposite sides of the structure = compressive force/cross-sectional area

Shear – 2 externally applied forces that equal, parallel, and applied in opposite directions but not
in the same line.
Plastic Region
Yield Point or
Elastic Limit
Stress or
Load
Ultimate Failure or
Fracture Point
Elastic Region
Strain or Deformation
Elastic Range – no permanent deformation occurs
Yield Point – point at which permanent deformation will begin
1
Plastic Range – if structure is unloaded, permanent deformation results
Stress/Strain of Various Materials
Plastic Region
Metal
Glass
Stress
Bone
Rubber
Strain
Young’s Modulus = slope in the elastic region = stress/strain
 stiffness of material   Young’s Modulus
Viscoelasticity – considers 2 properties of a material


Elasticity – ability to return to its original shape following deformation after the removal of the
deforming load
 Non-time dependent – returns
 Stores energy (RUBBER BAND)
Viscosity – a material’s ability to dampen/lessen shear forces
 time and rate dependent properties
Viscoelastic – sensitive to the duration of the force application
Creep – occurs when a viscoelastic solid is subjected to a constant load

Typically responds with a rapid initial deformation followed by a slow, time-dependent, increasing
deformation until equilibrium is reached.
RAPID INITIAL DEFORMATION  SLOW, INCREASING DEFORMATIONEQUILIBIUM
(CREEP)
2
Creep
Deformation
Time
Hysteresis
Viscoelastic materials do not store all of the energy that is transferred to them when deformed by an
applied force. Energy is transferred into another form and not available for recovery.
LOSS (TRANSFER) OF ENERGY = ENERGY EXPENDED – ENERGY REGAINED (HYSTERESIS)
Example
Muscle –
When muscle is loaded via an eccentric contraction some energy is stored in the series elastic component
(SEC) of the muscle (actin and myosin fibers), and some is lost as heat.
Stretch Muscle – transfer of energy into heat  could be detrimental (inflammation)
Loading
Load
Unloading
Hysteresis – loss (transfer) of energy
Deformation
Connective Tissue
Ligaments, tendons, bones, synovium, labra, cartilage, bursa, fat pads, etc.
3
Composed of two parts:
1. Extra-cellular matrix
2. Cells – blast and clast –type cells for synthesis and maintenance of extracellular matrix, also
defense-like cells.
The specific composition and proportions of these components is dependent on the function of the
connective tissue.
Extra-cellular matrix
1. Non-fibrous – ground substance (proteins) – glycoproteins and proteoglycans
 Functions – water binding, support, and protection
2.
Fibrous
 Collagen (white protein) – most abundant (30% of all protein in mammals)
 Non-elastic – often oriented/configured to allow for elastic-like qualities
(crimp).
 Elastin (yellow protein) – elastic properties
Biomechanics of Bone
Bone – hardest connective tissue in the body
Look at its biomechanical functions and you will know why:
1. protection
2. link
3. attachments for muscles
4. facilitate movement as levers (rigid)
Components of Bone

Inorganic – rigid/hard (minerals) Ca and PO3 (65-70% of dry wt.)

Organic – flexible/resilient (protein) – collagen fibers (25-30 % of dry wt.)
 Collagen composes 95% of extracellular matrix

Ground Substance – Glycoaminoglycans (GAG) cementing substance
 5% of extracellular matrix

Water – 25% of weight, 85% of the water is found in the organic matrix

Cells – osteoblasts/clasts, fibroblasts/clasts
Fundamental unit of bone is the osteon or haversian system
 Concentric layers/lamellae

Collagen is intertwined in the osteons which increases the resistance to mechanical stresses
Types of bone
Cortical/Compact Bone – OUTER – 5-30% porosity  more dense
Withstands compression > tensile > shear
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Cancellous/Trabecular/Spongy- INNER – 30-90% porosity
Highly Responsive to the loads placed on it (Wolff’s Law), therefore which forces it withstands best is
varies (compression and tensile)
Mechanical behavior (behavior due to forces and moment/torque) of bone is affected by:
1.
2.
3.
4.
5.
loading mode – type of force/torques
rate of loading
frequency of loading
geometric characteritics
mechanical properties of materials
1.
Loading modes
a.
tensile – Base of 5th metatarsal @ attachment of the peroneus brevis tendon, Calcaneous @
attachment of Achilles (gastro/soleus)
What can be done to reduce the load at the site of attachment? Heel lift for achilles problem while
healing
b.
compressive – vertebrae secondary to muscular contractions/lifts and femoral neck fractures
secondary to osteoporosis
With elderly individuals who suffer a hip fracture, how and when does the hip actually fracture?
What forces are better to increase bone content?
How much force is too much?????
c.
shear – tibial plateau fracture (fractures occur mostly in cancellous bone)
d.
bending – bending about an axis resulting in tensile and compressive forces

3 point bending

4 point bending – dual force couple

magnitude is proportional to their distance from the axis
Skier’s Fx
Examination of the knee:Valgus versus varsus stresses in the knee?
The use of these concepts in orthotics fabrication
5
e.
torsion – twisting/torque/moment about the logitudinal axis
 magnitude is proportional to the distance from the axis
f.
combined loading – explains most fractures
2. Rate of Loading
Since bone is viscoelastic its behavior varies with the rate at which it is loaded
High loading Rate
Load
Low loading Rate
Deformation
Load to failure rate almost doubled (bone was actually 50% stiffer)
3.
Frequency of Loading
Load
Injury
Repetition
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Stress/Fatigue Fracture Model
Strenuous Exercise
Fatigued Muscle
Loss of Shock Absorbing Capacity
Rely on passive
elements as opposed to
active and passive
Altered Gait
Abnormal Loading
Altered Stress Distribution
High Compression Combined  High Tension
Slow  Process  Fast
Oblique Cracks
Debonding of osteons / transverse cracks
Oblique Fracture
Transverse Fractures
Repetition is often the evil - HNP
Mechanism for other types of injuries in the body – OA, RSI, CTD
4.
Geometric Properties of the object


Stress = force/area (large the cross-sectional area stiffer and stronger the bone)
Longer the bone the more susceptible to bending moments

Iatrogenically induced
 Stress Raisers (length of defect < diameter of bone) –screws and empty screw holes
 Reduction in the energy storage capability and overall strength
 Open section defect ( length > diameter)
Torsional type forces appear to be worst
Effect of Bone Remodeling on Geometry
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Load Deformation Curve
Effects of Immobilization on Bone in Rhesus monkeys
Normal
Load
Immobilized
Deformation
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