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Lecture  2  

Building  stones  of  the  human  body:  bone,  car?lage,  tendons  and  

ligaments    

Bone  (Ref.  N&F:  first  part  of  chapter  2,  E&S  chapter  9)    

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Bone  material  

!

Duc?le  –    large  plas?c  deforma?on    BriNle  –    

no  plas?c  deforma?on    

A  long  skeletal  bone  

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!

Blood  vessel

Small  channels

Hollow  space

Bone  cells

Periost

!

Cor?cal  bone  (compact  bone)  

Diameter  of  an  osteon:    around  0.2  mm  

!

Cancellous  bone  (spongy  bone)  

!

Femoral  head  

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Cor?cal  vs  cancellous  bone  

Stored

 ene

rgy  

Stored  energy  

Anisotropic  material  behaviour    

!

femoral  shaT  (lårbenshals)    

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Different  loading  cases  

•  Compression  •  Tension  •  Bending  •  Shear  •  Torsion    …  or  in  combina?ons!  

How  much  can  bone  take?    •  σu≈  200  MPa  in  compression  •  σu≈  130  Mpa  in  tension  •  σu≈  65  MPa  in  shear  (adult  cor?cal  bone)  

Failure  modes  

!

Tension:  debonding    

!

Tensile  fracture  through  the  calcaneus  caused  by  strong  contradic?on  of  the  Achilles  tendon.      

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Failure  modes  (cont.)  

!

Compression:  cracking    

!

Compression  fractures  of  the  femoral  necks  (electric  shock  theraphy)      

Car?lage  (in  brief)    

Car?lage  cell  -­‐  chondrocyte  

Elas?c  threads  -­‐collagen  

Surrounding  substance  –  chondroi?n    

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Ar?cular  car?lage  

!

Articular  cartilage

Func?on:  •  spread  out  the  loads  •  allow  rela?ve  mo?on  with  minimum  fric?on  and  wear  socket

Synovia  (ledvätska)   Capsule  

(ledkapsel) ball

!

Tendons  (senor)  •  Cells:  tendocytes  •  Extracellular  matrix  (ECM):  

collagen,  elas?n    

Tendons  and  ligaments  (Ref.  N&F:  chapter  4,  E&S  chapter  9)    

Ligaments  •  Collagen,  elas?n,,  

proteoglycans  

Anterior  cruciate    ligament  

(främre  korsbandet)  

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 •  Protein    •  Trippel  helix  of  polypep?de  

chains    •  Can  be  found  in  bone,  

tendons,  intervertebral  discs,  ligaments  and  skin  

 

Collagen  

 •  Protein.  •  Can  be  founded  in  skin,  

walls  of  blood  vessels,  ligaments.  

•  A  liNle  bit  viscoelas?c    

Elas?n  

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Tendon  

!Tendon  sheath  (senskida)  

Ligaments  

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Fiber  structures  

Unloaded  ligament

Loaded  ligament

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Tension  tests  of  two  different  ligaments    

Much collagen

Much  elastin

From:  Illustra?ve  examples  Biomechanics, LTH, 2015

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5. Consider the question of the strength of human tissues and their margin of safety when we exercise. Take the example of the tension in the Achilles tendon in our foot when we walk and when we jump. The bone structure of the foot is shown the figure. To calculate the tension in the Achilles tendon we may consider the equilibrium of forces that act on the foot. The joint between the tibia and the talus bones may be considered as a pivot.

6. The head in the picture below is considered as a rigid body for the present purpose. It rocks on the occipital condyles C where an axial force FA, a shear force, V, and a neck torque To, resist motion. An uppercut (treated as an instantaneous load B at an angle of 63o to the horizontal) is applied to the chin, and the initial linear acceleration, a, of the mass centre, G, is photographically determined to be 140g. For a head mass of 3.5 kg, a moment of inertia about an axis perpendicular to the sagittal plane of 0.0356 kg m2, and the dimensions shown, what are the reactions at the occipital condyles if torque T0, which requires muscle activation, is temporarily neglected?