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Residual stress

O. B. A. 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 can. be quantified by measuring opening angle. O. B.

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Residual stress

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  1. O B A 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 can be quantified by measuring opening angle

  2. O B A Why is residual stress important? • 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

  3. 120 No residual stress: sinner/smean = 6.5 Residual stress: sinner/smean = 1.4 80 40 0 Residual stress evens out the stresses in the vessel wall Circ. Stress (s) [kPa] 1 1.1 1.2 Inner Outer Normalised radius

  4. Pressurised tubes Heat Cool

  5. Stretch steel while Concrete sets When concrete sets, tension in steel bends beam 16 tons Beam withstands higher Load without bending Steel rod Wet concrete in a mold

  6. Residual strain in vegetables

  7. With thanks to Stephen Gottlieb

  8. 1 mm Rat aorta 5 1 2 6 3 7 4 8

  9. 0 10 20 30 40 50 60 Rat aorta 160 120 Opening angle [°] 80 40 No sex differences 0 Age [weeks]

  10. 300 200 100 0 0 20 40 60 80 100 Human aorta Males Females Opening angle [ ° ] Age [yr]

  11. 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

  12. Artery lathe

  13. Artery lathe

  14. Material removed from outside 200 Material removed from inside Material removed from both sides 100 Opening Angle [degrees] 0 -100 1.0 0.5 0.0 Fraction of vessel remaining Localisation of residual strain Greenwald, S. E., et al. (1997). ASME Journal of Biomechanical Engineering 119: 438-444.

  15. After elastase treatment Original

  16. After collagenase treatment Original

  17. Original Minutes after freezing Months after freezing

  18. FROZEN CONTROL 0 20 40 60 80 100 200 150 Opening Angle (°) 100 50 0 Position (%)

  19. Entire aorta 1.25 Thoracic Abdominal 1.00 0.75 0.50 0.25 0.00 OA ratio [Treatment/Control] Collagenase Elastase Freezing

  20. 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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