Presentation is loading. Please wait.

Presentation is loading. Please wait.

Tendon. Outline: – Function – Structure – Mechanical Properties – Significance to movement.

Similar presentations


Presentation on theme: "Tendon. Outline: – Function – Structure – Mechanical Properties – Significance to movement."— Presentation transcript:

1 Tendon

2

3 Outline: – Function – Structure – Mechanical Properties – Significance to movement

4 Function Connect muscle to bone, but are not rigid Are quite stretchy Passive but important Not just rigid, passive structural links b/n muscle and bone, but also affect movement through the overall function of the muscle-tendon-unit. Function: – transmit muscle force and slide during movement – Store elastic energy Tendon properties affect force transmitted from muscle to bone

5 Structure Primarily collagen : a structural protein Collagen fibril -> fascicle->tendon Bad blood supply -> slow to heal

6 Parallel bundles of collagen fibers Resist stretching along long axis of tendon Sufficiently flexible

7 Tendon Outline: – Function – Structure – Mechanical Properties – Significance to movement

8 Mechanical Properties Many experiments on isolated tendons Show same mechanical property across different tendons

9

10 Tendon or ligament “J-shaped” Stiffness (k) = slope – units = N/m Stiffness: force required to stretch tendon/ligament by a unit distance Force per change in length Hooke’s Law – F=kx F=elastic force x=amount of stretch k=stiffness Force Displacement (  x) Toe region Linear region

11 Tendons/ligaments are viscoelastic Purely elastic materials – force-displacement relationship does NOT depend on velocity of stretch or time held at a length or load Viscoelastic materials – force-displacement relationship DOES depend on: Velocity of stretching Time held at a given length or load Think of other materials that are viscoelastic?

12 Tendons are viscoelastic Nonlinear response Hysteresis Velocity dependent loading Creep Load relaxation

13 Viscoelasticity trait #1: Nonlinear Response “J-shaped” Stiffness (k) = slope – units = N/m Stiffness: force required to stretch tendon/ligament by a unit distance Force per change in length Hooke’s Law – F=kx F=elastic force x=amount of stretch k=stiffness Force Displacement (  x) Toe region Linear region

14 Viscoelasticity trait #2: Hysteresis (Stretch & recoil: ) Displacement (x) Force Stretch Recoil Hysteresis: Force vs. displacement different for stretch & recoil

15 Viscoelasticity trait #3: velocity dependent stiffness From Wainwright et al. (1976). “Mechanical design in organisms”. Displacement Force Fast stretch Slow stretch At faster stretching velocities: 1. More force needed to rupture tendon

16 Viscoelasticity trait #4: Creep Displacement Time Stretched with a constant force & displacement measured – Length increases with time

17 Viscoelasticity trait #5: Load relaxation Specimen held at a constant length & force measured Force Time 2-10 min ( N & F, Fig 3-10)

18 Elastic energy Stretch: mechanical work done on tendon/ligament equals elastic energy storage – Area under force - displacement curve Force Displacement Elastic energy stored during stretch

19 Viscoelasticity trait #3: velocity dependent stiffness From Wainwright et al. (1976). “Mechanical design in organisms”. Displacement Force Fast stretch Slow stretch At faster stretching velocities: 1. More force needed to rupture tendon 2. More energy is stored

20 Elastic energy Stretch: mechanical work done on tendon/ligament equals elastic energy storage – Area under force - displacement curve Recoil: material returns some (most) of energy stored elastically during stretch

21 Elastic energy returned during recoil Mechanical energy stored & returned by tendon/ligament Force Displacement Force Displacement Elastic energy stored during stretch

22 For normal stretches, 90-95% of the elastic energy stored in tendons & ligaments is returned Force Displacement Energy lost Larger hysteresis loop - greater energy loss Hysteresis: indicates “viscoelasticity”

23 Elastic energy Stretch: mechanical work done on tendon/ligament equals elastic energy storage – Area under force - displacement curve Force Displacement Elastic energy stored during stretch Area = A) ½ Fx B) ½ kx C) ½ kx 2 D) A & B E)A & C (x,F)

24 Achilles elastic energy storage during stance phase of run FgFg Example of important equations: U elastic = 0.5 k (  L) 2 F = k  L Known: k Achilles = 260 kN/m F = 4700 N U elastic = ? A)2.34 B)42120 C) 42 D)0.042 E) None of the above F Achilles

25 Strain Can measure length change in terms of mm But more useful as % of original length, so can compare tendons of different lengths Strain (  ) = L-L o /L o – L: current length – L o :original length ‘stretchiness’

26 Stress Because tendons have different thickness, want to normalize force as well – Thicker tendons need more force and vice versa – So normalize by area – Stress (  )=Force/Area

27 Stress/Strain (  ) By normalizing stress and strain, can now compare properties of materials of different sizes and shapes, regardless of absolute shape Measure intrinsic tendon properties

28 Stress/Strain Relation for Tendon/Ligament Injury Failure (rupture) Stress  (MN/m 2 ) Strain  100 8% Elastic region Plastic region Toe region E    yield  failure

29 Stress vs. Strain for tendon/ligament Similar for all mammalian tendons & ligaments Elastic modulus: slope E=stress/strain, =  – units of Pascals (N/m 2 ), same as stress – kPa, Mpa, GPa Strain (%) Stress (MN/m 2 ) Stretch Recoil 70 5 35 2.5 0 0

30 Compare the stiffness of a rubber band and a block of soft wood A) rubber band is more stiff B) rubber band is less stiff C) stiffness is similar D) Not enough information

31 Can compare different materials easily Tendon E = 1 GPa Soft wood (pine) E = 0.6 GPa Passive muscle E = 10kPa Rubber E = 20kPa Bone E= 20 GPa Walnut E= 15 Gpa Diamond E= 1000 Gpa Jello E = 1Pa

32 Stress vs. strain: material not geometry Two important definitions: Stress = F / A F = force; A = cross-sect. area Units = N / m 2 = Pa Strain (%) = (displacement / rest length) 100 = (  L / L) 100

33 Stiffness vs. Elastic Modulus Elastic Modulus (a.k.a. “Young’s Modulus”) – Slope of stress-strain relationship – a material property Stiffness – Slope of force-displacement relationship – depends on : material (modulus) & geometry Structural property

34 Stress/Strain vs Force/Length Material property vs. structural property Stress/Strain ind of geometry Force/Length (stiffness) depends on geometry.

35 Geometry effects Stress = Elastic modulus Strain  F / A = E ∆L / L Force = Stiffness displacement  F = k∆L Combine (1) & (2) to find: k = EA/L – E: similar in all tendons/ligaments  A or  L causes  k

36 Extending the stress-strain relationship to injurious loads for tendon/ligament Injury Failure (rupture) Stress (MN/m 2 ) Strain 100 8% Elastic region Plastic region

37 Stress/Strain vs Force/Length Material property vs. structural property Stress/Strain ind of geometry Force/Length (stiffness) depends on geometry.

38 Tendon strain Achilles tendon during running: ~ 6% – close to strain where injury occurs (~ 8%) Wrist extensor due to muscle force (P 0 ): ~ 2%

39 Tendon Outline: – Function – Structure – Mechanical Properties – Significance to movement

40 We need tendons with different stiffnesses for different functions. How is this accomplished? Possibilities: – different material properties – different geometry (architecture)

41 High force vs. versus fine control Muscles in arm/hand demand fine control – precision more important than energy Slinky vs. rope

42

43 Ankle extensor tendon vs. wrist extensor tendon Wrist extensor – k = 15 kN/m – F (muscle) = 60 N –  L = F / k = 0.004 m Achilles tendon – k = 260 kN/m – F (muscle) = 4.7 kN –  L = F / k = 0.018 m Force Displacement Achilles Wrist ext.

44 Basis for tendon stiffness variation? – different material properties? – different geometry (architecture)?

45 Achilles tendon vs. wrist extensor tendon Achilles tendon vs. wrist ext. tendon – k: 17 times greater Geometric differences? – A: 30 times greater – L: 1.75 times longer k = EA/L E ~ 1.5 GN / m 2

46 F = k  L Elastic Energy = 0.5 k (  L) 2 Elastic Energy = 1/2 F  L k =  A/L  elastic modulus = stress/strain ~ 1.5 x 10 9 N/m 2 for tendon stress = F/A strain =  L/L 10,000 cm 2 = 1 m 2 Useful tendon equations

47 E = 1.5 x 10 9 N/m 2 for both tendons wristAchilles L = 0.17 mL = 0.29m A = 1.67 x 10 -6 m 2 A = 0.00005 m 2 k = EA/L = 15 kN/m k = EA/L = 260 kN/m elongation for 60N load? elongation for 4,700N load?  L = F/k = 0.004mF/k = 0.018m Strain? =  L/L = 0.004 / 0.17 = 2.4% = 0.018 / 0.29 = 6.2% Human Tendons Compared

48 Problem Solving Approach Write down what is given Write down what you need to find Write down the equations you will use Show work! – Step by step

49 Design a wrist extensor tendon that when loaded with 60N of force will undergo the same %strain (6.2%) as the Achilles tendon. (Given L, determine A) L=0.17 m Practice Problem

50 If the wrist extensor tendon in the example had a cross sectional area = to the Achilles tendon example, what would be the absolute length change with a load of 60 N? Given: A achilles = 0.00005 m 2 ; L wrist = 0.17m Practice Problem


Download ppt "Tendon. Outline: – Function – Structure – Mechanical Properties – Significance to movement."

Similar presentations


Ads by Google