residual stress force remaining in a body when all external loads are removed gives rise to a...
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Residual stress
• Force remaining in a body when all external loads are removed
• Gives rise to a residual strain (movement) which can be measured and used to estimate the degree of residual stress
• In arteries, residual strain canbe quantified by measuring opening angle
A
O
B
• Helps to balance forces within the arterial wall
• Controls the remodelling process by altering the local loading on VSMC
• Required to define the zero stress state
A
O
B
Why is residual stress important?
0
40
80
120
1 1.1 1.2
Circ. Stress [kPa]
Inner OuterNormalised radius
No residual stress: inner/mean = 6.5
Residual stress: inner/mean = 1.4
Residual stress evens out the stresses in the vessel wall
Pressurised tubes
Heat
Cool
Steel rod
Wet concrete in a mold
Stretch steel whileConcrete sets
When concrete sets, tensionin steel bends beam
Beam withstands higherLoad without bending
16tons
Residual strain in vegetables
With thanks to Stephen Gottlieb
1
2
4
3
7
5
6
1 mm 8
Rat aorta
6050403020100
0
40
80
120
160
Age [weeks]
Ope
ning
ang
le [
°]
Rat aorta
No sex differences
6543210
100
200
300
MALE
FEMALE
Position
Angle (°)
(A)
1008060402000
100
200
300
Age [yr]
Males
Females
Ope
ning
ang
le [
° ]
Human aorta
Where does residual stress reside?
• Which part of the wall– Selective removal of layers, by lathing frozen
specimens
• Which components of the wall– Selective digestion/destruction experiments,
using enzymes to remove elastin/collagen and freezing to destroy muscle
Artery lathe
Artery lathe
Fraction of vessel remaining
Ope
ning
Ang
le [
degr
ees]
1.0 0.5 0.0
0
100
200
-100
Material removed from outside
Material removed from inside
Material removed from both sides
Localisation of residual strain
Greenwald, S. E., et al. (1997). ASME Journal of Biomechanical Engineering 119: 438-444.
Original
After elastase treatment
Original
After collagenase treatment
Original
Minutes after freezing
Months after freezing
1008060402000
50
100
150
200COLLAGENASE
CONTROL
Position (%)
ANGLE ENZ
1008060402000
100
200ELASTASE
CONTROL
Position (%)
Opening Angle (°)
1008060402000
50
100
150
200FROZEN
CONTROL
Position (%)
Op
en
ing
An
gle
(°)
0.00
0.25
0.50
0.75
1.00
1.25
Collagenase Elastase Freezing
Entire aorta
Thoracic
Abdominal
OA
rati
o [
Tre
atm
ent/
Contr
ol]
Residual stress: conclusions
• Increases with age
• Greater in men than women
• Compressive at inner side of vessel wall
• Tensile at outer side
• Resides primarily in the elastic component– and to a lesser extent, in muscular component
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