Biomechanics Flashcards
What is an isotropic material?
- The material behaves similarly in all directions of force
- e.g. metals / alloys
What is an anisotropic material?
- A material shows directionally dependent behaviour e.g most living tissue. -cortical bone
Define stress ?
- Force per unit area
- In Newton / metre 2
What is strain?
- Change in length of a material/ original length
- it has NO UNITS
- doesn’t take into account x sectional area of material
What is young’s modulus?
- Stress /strain
- N/m2
- Gradient of stress/ strain graph
- idea of stiffness I material
What is stiffness?
- Deflection under a given load.
- The steeper the stress- strain curve the stiffer the material .
- The less steep the curve the more flexible the material
What is the Yongs modulus of
cartilage
Tendon
Cancellous bone
UMWPE
Pmma
bone cement
Cortical bone
Ti alloy
Stainless steel
Colballt chrome
cartilage 0.02
0.5 Cancellous bone
1 UMWPE
Pmma bone cement 2
Cortical bone 20
Ti alloy 100
Stainless steel 200
Cobalt chrome 200
What is hook’s law
- Where stress is proportional to strain such that deformation is recoverable- elastic portion of graph
What is yield stress ?
- The stress necessary to produce a specific amount of permanent deformation
What is yield point?
- Point in the graph where plastic deformation starts-
- the point at which further deformation is no longer recoverable
- In ortho this is close to the yield stress
What’s is strain hardening?
- Where plastic deformation actually increases Materials resistance to further deformation
- e.g. cold working of metal alloys
What is fracture stress?
- A stress level at which a material’s integrity is breeched and is fractured
What is the ultimate tensile stress?
- The max amount of stress a material can with stand before fracture is imminent
What is brittleness ?
- Brittle materials do not deform plastically but display elastic behaviour right up to failure- e.g ceramic
- yield stress almost = to fracture stress
What is ductility ?
- A ductile material undergoes a large amount of plastic deformation before failure- e.g.metals
What is strain energy?
- The area under a stress- strain curve.
- Combines recoverable strain energy - elastic region of curve and absorbed strain energy ( plastic region of curve)
What is toughness?
- The energy per unit volume that a material can absorb before failure.
- The area under a stress/ strain graph
What is hardness?
- Ability of the material to resist stratching and indentation on the surface
What is fatigue failure ? How is it demonstrated?
- Failure of a material with repetitive loading at stress levels below the ultimate tensile strength
- In a SN CURVE LOG STRESS VS LOG OF NUMBER OF CYCLES ( millions)
What is the endurance limit ?
- Stress at which a material can withstand 10 million cycles without experiencing Fatigue failure typically hip operate above endurance limit, TKR operate at limit esp polyethylene -> fatigue failure
In regard to materials shape what is stiffness and rigidity ?
- Stiffness-the materials Ability to resist deformation
- Rigidity- the structures ability to resist deformation
What is notch sensitivity ?
- **Is the extent at which the sensitivity of a material to fracture is increased by the presence of a surface inhomogeneity **
- eg ductile materials (SS) have low notch sensitivity cf brittle materials such as ceramic/titanium have HIGH notch sensitivity
What is Viscoelasticity?
- Time dependent behaviour which is characterised by
- CREEP
- STRESS RELAXATION
- TIME DEPENDENT STRAIN BEHAVIOUR
- HYSTERESIS
- ie in CARTILAGE, LIGAMENTS AND INTERVERTEBRAL DISCS
What is creep?
- Time DEPENDENT DEFORMATION IN RESPONSE TO A CONSTANT LOAD
What is stress relaxation ?
- TIME DEPENDENT DECREASE IN LOAD REQUIRED TO MAINTAIN A MATERIAL AT A CONSTANT STRAIN
What is hysteresis?
- The difference in a stress strain curve between loading and unloading is due to strain energy lost in heat from internal friction forces
What is bending rigidity?
Second moment of area x young’s modulus Incorporates the materials shape, size and structure Ie choosing a material that is stiff x2 chrome cf Ti makes a rectangular plate have a increased sma and. So rigidity increased by a third power ie 2 to the power 3 = 8
Describe time dependent strain behaviour?
- Behaviour of plastine
- Gradually pull apart a blob of plastine -> a long thin thread of plastine before it eventually breaks into two
- however if we pull the plastine apart quickly, then the plastine breaks quickly
- the strength required to break the plasticine is higher when pulling the plastine apart
- the rate of change of length of plasticine ( the strain rate) affects the behaviour
- the faster the strain rate m the higher the stress at a given level of strain
- conversely a low strain rate requires more time but less stress to fx the material
When do tensile stresses occur?
When 2 forces pull away from each other along the same line
When do compressive stresses occur?
When 2 forces push towards each other along the same libe
What is Hooke’s Law?
The force needed to extend or compress a spring by some distance is proportional to that distance. That is, F= Kx where k is a constant factor characteristic of the spring, its stiffness ie stress proportional to strain- the linear portion of the stress/strain graph where Young’s modulus is constant
Draw a stress -strain curve and label the regions?
Diagram
What is the elastic region?
What can you determine here in this part of the graph?
The stress- strain relationship is linear.
Hooke’s law is obeyed- stress proprtional to strain Young’s Modulus- the stiffness increases as the gadient of the line increases ALL the deformation in this part of the graph is ELASTIC ie RECOVERABLE
What is the toe region? name an example?
- The initial portion of the curve where there is a no linear relationship uncrimping of collagen fibres in tendons- as the tendon is stretches the collagen unfurl until they are straight and then stiffness increases quickly
What is the plastic region of the graph? Where does this commence from?
AT this point further deformity is NO LONGER RECOVERABLE ie PLASTIC At the YIELD POINT
What is the YIELD POINT?
Where there is A DRAMATIC INCREASE IN STRAIN WITH LITTLE INCREASE IN STRESS
What follows the yield point?
A PEFECT PLASTIC REGION then a region where STRAIN HARDENING occurs
What is the STRAIN HARDENING ?
The phenomon where PLASTIC DEFORMATION ACTUALLY INCREASES THE MATERIALS RESISTANCE TO FURTHER DEFORMATION e.g.- COLD WORKING OF ALLOYS
What is YIELD STRESS?
The STRESS NECESSARY TO PRODUCE A SPECIFIC AMOUNT OF PERMANENT DEFORMATION i.e 0.002 - 2%- very close in ortho to the yield point
What is strength of a material?
- It represents the DEGREE OF RESISTANCE TO DEFORMATION OF A MATERIAL
- a material is strong if it has a high ULTIMATE TENSILE STRENGTH
What is Hardness of a material?
The SURFACE PROPERTY OF A MATERIAL; THE ABILITY OF A MATERIAL TO RESIST STRATCHING AND INDENTATION ON THE SURFACE not determined by the stress strain curve
What are the underlying mechanisms responsible for disco-elastic behaviour?
FRICTION internally between micro-elements in the structure. Movement of interstitial fluid through the material creates a drag that produced the viscoleastic behaviour
What is a shearing force?
- IS A force applied PARALLEL to or in line with the SURFACE OF AN OBJECT
When do SHEAR FORCES occur?
- 2 FORCES are directed to parallel to each other but not along the same line or the same direction
When do tensile stresses occur?
- When 2 forces pull away from each other along the same line
What is shear modulus?
- Shear modulus = shear stress/ Shear strain
- shear modulus is between 30-50% of the elastic modulus for most materials
- bone is weakest against shear forces ( also tensile), while strong in compression
- Bone tends to fail in shear
What is the neutral axis of a beam?
- A cross section area of a beam, there is graduation of stresses from extreme edges of the beam, where the compressive ( posterior) and tensile forces ( anterior) respectively towards the centre of the beam.
- The midpoint where there is no resulting force is the neutral axis
How do we calculate the bending stress?
- Applied force x distance from neutral axis
second moment area of material
what is the second moment area of material?
What affects it?
- Is a variable that decribes the spatial distribution of a material within a structure
- the type of material does not affect the SMA
- Organisation and shape of the material affects SMA
What is the second moment area of material for a rectangle?
- The perpendicular distance away from the neutral axis h has a third power effect on SMA
what is the second moment area of material for a solid circular cross section?
- The radius ( which the distance from the neutral axis) has a 4th power effect on the SMA
What is the effect on SMA with a hollow circular cross section?
- The total SMA = the SMA of the Solid portion - SMA of the missing inner hollow portion
What is the larger SMA for a solid or hollow pipe?
- Comparing the SMA of a solid rod to a hollow rod, the SMA is larger for the hollow pipe
- As a result the hollow pipe deforms less ( ie stronger) than the solid pipe of the same cross sectional area
- e.g as bone ages the outward appostional growth enlarges the medullary canal and increases the overall girth of the whole bone.
- this increase the SMA and with it the strength and resistance to fatigue to fx
What is bending rigidity?
- SMA x Youngs modulus
- rigidity then incorporates both the nature of the material and its shape, size and structure
- e.g doubing the thickness of a rectangular plate -> increase in SMA and increase rigidity by a third power of the multiplication
- ie doubling plate 23 = 8
What is a torsional force?
- Equal and opposite shear forces as applied to a cyclinder constrained in space-> twist= torsional force
How do you calculate the shear stress generated by the torque forces at any given point ?
- Shear stress= Applied torque x distance from axis of twist/ polar moment of intertia
What is the polar moment of internia?
- Similar to SMA
- is a variable parameter related to size and shape of a structure but not the material from which it is constructed
What is torsional rigidity?
- = PMA x Shear modulus
- a measure of the resistance of a material in a particular size nad shape to torsional forces
- so a cylinder the PMA varies to the power 4 radius
- so IM rod that is tiwce at thick has 24=16 x the rigidity
- when cf nails of the same diameter & length , cannulation or slotting of the nail decreases the PMA according to the earlier formula
- so torsional rigidity of slotted nails is lessened although bending ridigity is affected only minimally
