Skeletal considerations of movement
Long Bones
1)Shaped as an arch for distribution of forces. 2)Strongest along the axis. 3) epiphysis -in both ends ends of bones -spongy bone . 4)Metaphysis- compact bone 5) Diaphysis- medullary cavity.
Cancellous Bone
* 20% of skeleton weight. a )Spongy bone; end of bones , vertebrae, scapulae, pelvis. b) Porosity > 70% c) Trabeculae - small flat beams of bone. 1)Collagen runs along the axis of trabeculae providing tensile and compressive resistance. 2) Random directions provide strength.] 3) High fracture incidence due to mineral loss and alas compressive strength.
Work energy (stored mechanical energy) is calculated ...
-- stored as potential energy in the strained material can be calculated as the area under stress strain curve.
The yield strength is the stress required to produce
-----a small-specified amount of plastic deformation. The definition of this property is the offset yield strength determined by the stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by a specified strain.
the rate of strain hardening diminishes up to UTS.
.Beyond UTS the materials strains soften, so that each additional strain requires a smaller stress.
Flat bones
1) 2 layers of cortical bone w/ cancellous bone in between. 2) Protects internal structures. 3) offers broad surfaces for muscular attachment.
Irregular Bones
1)Cancellous bones w/thin layer of cortical bone. 2)Shape defined by function. Skull, pelvis , vertebrae.
Two types of Osseus tissue
1)Cortical compact, dense, outer layer 2) Cancellous spongy, very porous, inferior filling.
Stress—Strain Behavior
1)Elastic deformation. When stress is removed, material returns to original dimension. Deformation is reversible, non permanent. 2) Plastic deformation. When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation.
Material types
1)Elastic: linear - stress/ strain. Instant response to load. 2) Viscous a)Time dependent response to load. b) deformation remain after load removed 3)Viscoelastic a) hysteresis - energy lost during creep. b) resist shearing. c)effective stiffness depends on rate of applied load. d) time dependent response to load- some instantaneous strain then creep to a maximum strain.
The stress to produce continued plastic deformation increases with ,,,
1- increasing plastic strain, i.e., the metal strain-hardens. 2-Volume remains constant during plastic deformation, A·L = A0·L0 ; as the specimen elongates, it decreases uniformly along the gage length in cross-sectional area.
Elastic Modulus E or Young Modulus ?
1- slope of the elastic portion of the curve (the steep, linear region) E is proportionality constant during elastic deformation: σ = Eε. follows Hookes Law where s(sigma)= k.e (strain). K (the slope) is the elastic modulus. K is the stifness gradient
Stress vs Strain in the elongation curve?
1- stress and strain are obtained by dividing the load and elongation by constant factors, the load-elongation curve will have the same shape as the engineering stress-strain curve. The two curves are frequently used interchangeably.
NECKING or thinning down (locally slightly weaker)
1-Plastic deformation is concentrated here Initially the strain compensates for the decrease in area . engineering stress (proportional to load P) continues to rise with increasing strain. Eventually a point is reached where the decrease in specimen cross-sectional area is greater than the increase in deformation load arising from strain hardening. All further plastic deformation is concentrated in this region, and the specimen begins to neck or thin down locally.
Elastic limit
1-greatest stress material can withstand without measurable permanent strain. in engineering s-e curve elastic limit > greater than the proportional limit.
Fracture point ?Because the cross-sectional area now is decreasing far more rapidly ...
1-strain hardening increases the deformation load, 2-the actual load required to deform falls off 3-engineering stress continues to decrease until fracture occurs.
Bone tissue composition.
2 types of osteocytes bone cells : 1)Osteoblasts - create bone 2) Osteoclasts - resorb bone
Measures of Ductility
A high ductility indicates that the material is likely to deform locally without fracture . The measures of ductility are obtained from the tension test at fracture- The engineering strain - ef (called the elongation) and the reduction of area at fracture q are obtained after fracture .
Toughness.
Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve.
an appreciable fraction of the plastic deformation
Because an appreciable fraction of the plastic deformation will be concentrated in the necked region of the tension specimen. The engineering stress-strain curve often is quite flat in the vicinity of necking The value of ef will depend on the gage length L0 over which the measurement was taken.
failure occurs because the metal actually gets stronger as it is bent.
Bending a metal adds defects to the material. As defects accumulate, the metal gets harder and stronger, Cracks form, leading to a "fatigue" failure.
the Skeletal system
Bones, cartilage, ligaments and joints. 20% of total BW. Material properties of bones are influenced by nutrition, physical activity, and postural habits.
Brittle vs Ductile Fracture
Brittle material has a larger UTS, but Ductile absorbs more energy.,
Strain (m)
Deformation caused by applied stress . E (epsilon) = L'-L0/L0
Ductile and Brittle MATERIALS
Ductile and Brittle • Perfectly elastic: σ=Eε • Perfectly plastic: σ=Y • Elastic and Perfectly Plastic
what is the instantaneous slope of the stress- strain curve?
E is the stifness , the instantneous slope of the s-e curve. In the linear region E- K Stress- s(sigma)= k.e (strain). K (the slope) is the elastic modulus
What is elastic potential energy?
Elastic potential energy is the potential energy associated with objects that can be stretched or compressed is called elastic potential energy.
Stress and Strain Diagram
Engineering Stress & Strain - Original Area, Ao • True Stress and Strain - Instantaneous Current Area,
Compression Properties
Engineering stress, σE = F/A0 • Engineering strain, e= h-h0/ h0 Barreling due to the friction At the contact surfaces. σ = K ε
Viscoelastic stress- strain hysteresis
Fish up shape- graph. Hysteresis - energy lost during creep. The material returns to original state unlike plastic deformation.
For ductile metals the tensile strength ....
For ductile metals the tensile strength should be regarded as a measure of the maximum load, which a metal can withstand under the very restrictive conditions of uniaxial loading.
Stress ( sigma) [N/m2] or {PA}
Force applied to deform a structure per unit area. stress= F/A
Yield stress (The stress at the yield point)
Hooke's law is not valid beyond the yield point. Yield stress, is an important measure of the mechanical properties of materials.,The yield stress is chosen as that causing a permanent strain of 0.002 (strain offset) The yield stress measures the resistance to plastic deformation.
Material Fatigue
If the stress enters the plastic region - residual micro-strains ( cracks, tears). if the stress is repeated over and over the material will fail at these micro-strains, at a much lower stress than UTS of the material
Yield point.
If the stress is too large, the strain deviates from being proportional to the stress. The point where this happens is the yield point b/c there the material yields, deforming permanently (plastically).
σe = Ee?
In the early (low strain) portion of the curve, many materials obey Hooke's law to so that stress is proportional to strain with the constant of proportionality being the modulus of elasticity or Young's modulus, denoted E:
In the elastic region ?
In the elastic region stress is linearly proportional to strain.
M or UTS>
In the engineering stress-strain curve, this point indicates the beginning of necking. The ultimate tensile strength is the maximum load measured in the tension test divided by the original area.
Offset Strain Method
In the stress strain curve , fit the low s(sigma) region to a straight line. Shift the line to the right until it intersects e (strain)= 0.002.The Yield Stress is found at the intersection of this line with the stress - strain curve.
Tension test?
In the tension test a specimen is subjected to a continually increasing uniaxial tensile force while simultaneous observations are made of the elongation of the specimen. An engineering stress-strain curve is constructed from these measurements.
Cortical Bone
Lamillae - hollow concentric tubes of parallel collagen fibers which run in different directions.
Function of the skeletal system
Leverage support protection storage blood cell formation
Elastic Properties of Materials
Materials subject to tension shrink laterally. Those subject to compression, bulge.
Short Bones
Mostly cancellous w / thin layer of cortical. a) main role is shock absorption and transmission of forces. ie patella- sesamooid - short bone embedded in a tendon to alter angle of insertion of muscle and diminish friction. More durable than tendon ligaments.
How to pinpoint s-y ( stress- yield point ?
Offset Strain Method for s-y. This point refers to where the change b/w linear and curved is. The offset strain method involves a 0.2% strain offset.
Bone composition
Organic collagen fibers, inorganic mineral salts.
Proportional limit
Proportional limit is the highest stress at which stress is directly proportional to strain. It is obtained by observing the deviation from the straight-line portion of the stress-strain curve.
Residual Strain?
Residual strain is created in the plastic region. It represents the difference between original length L0, and the length resulting from stress in the plastic region.
Lever
Simple machined that magnifies force and speed of movement, for example define it as a simple machined converting linear force to angular torque. Long bones utilize coverage.
Stored mechanical energy ?
Stored mech energy per unit volume of material .
what is Stress Force comparable to?
Stress force, like tension is the the force transmitted through the material as the stress inside the material . Stress force is equal and opposite in both ends.
Stress-Strain Relationships
Tensile Properties - Elastic modulus - ductility - hardness - various measures of strength • Proportional limit • Elastic limit • Yield strength • Offset yield strength • Ultimate Tensile strength, • Failure Strength Elongation (EL) =(Lf-Lo)/Lo Area Reduction (AR) =(Ao-Af)/Ao TS = Fmax/A0
The 0.2% offset yield strength?
The 0.2% offset yield strength is the stress value, σ0.2%YS of the intersection of a line (called the offset) constructed parallel to the elastic portion of the curve but offset to the right by a strain of 0.002. It represents the onset of plastic deformation.
Toughness
The amount of energy absorbBed before failure.
Strain energy
The area under the σe − e curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material in straining it to that value.
mechanical energy.
The energy acquired by the objects upon which work is done is known as mechanical energy. Potential energy (stored energy of position). A drawn bow possesses mechanical energy due to its stretched position (elastic potential energy).
The engineering stress?
The engineering stress is the load borne by the sample divided by a constant, the original area. The true stress is the load borne by the sample divided by a variable the instantaneous area. The True stress always rises in the plastic, whereas the Engineering Stress rises and then falls after going through a maximum.
Compression
The expression for deformation and a given load δ = P L/AE applies just as in tension, with negative values for δ and P indicating compression. The modulus E and the stress-strain curve simply extends as a straight line into the third quadrant
The fracture strain ?
The fracture strain is the engineering strain value at which fracture occurred.
Ultimate Tensile Strength (UTS)
The maximum load before necking occurs. Necking- the longitudinal point where the bar begins to have a different cross- sectional A.
The shape and magnitude of the stress-strain curve of a metal will depend on prior history of plastic deformation, strain rate, and state of stress imposed at testing.
The parameters, which are used to describe the engineering stress-strain curve of a metal, are the tensile strength, yield strength or yield point, percent elongation, and reduction of area.
Safety Factor. (Strength/ load.)
The stress factor is used for design of materials, and made to withstand 5-10x typical stress.
The tensile strength, or ultimate tensile strength (UTS)?
The tensile strength, or ultimate tensile strength (UTS), is the maximum load divided by the original cross-sectional area of the specimen.
The ultimate tensile strength is?
The ultimate tensile strength is the engineering stress value or σuts, at the maximum of the engineering stress-strain curve. It represents the maximum load, for that original area, that the sample can sustain without undergoing the instability of necking, which will lead inexorably to fracture.
Tensile strength.
When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength (sTS) , and then falls as the material starts to develop a neck and it finally breaks at the fracture point. Note that it is called strength, not stress, but the units are the same, MPa.
plastic deformation.?
When the load exceeds a value corresponding to the yield strength, the specimen undergoes gross plastic deformation. It is permanently deformed if the load is released to zero.
mechanical energy is stored within the material as strain energy.
When the stresses are low enough that the material remains in the elastic range, the strain energy is just the triangular area .
Measures of Yielding?
With most materials there is a gradual transition from elastic to plastic behavior, proportional limit, elastic limit, yield strength.
Elastic Region vs Force applied
Within the elastic region , where the force applied is removed the material return to its original state.
Elastic Region
Within the elastic region there is a linear relationship b/w Stress and Stifness
Plastic Region(b/w e-yield and e-failure
Within the plastic region = there is a non-linear relationship s= f(e)
Material properties of bone tissue .
a) low density b-high tensile high compressive strength. b)5-7% of bone mass is recycled every week c) significantly elastic d) constantly modified and remade.
Ultimate strength is an attribute related to a material, ((N/m2).)
ather than just a specific specimen made of the material, The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN/m2.
Engineering Stress & Strain
e = δ/L0 σe = F/A0
Bones increase in size
from superior to inferior in proportion to the amount of BW they bear.
the strain energy increases quadratically with the stress or strain;
i.e. as the strain increases the energy stored by a given increment of additional strain grows as the square of the strain.
The hysteresis of energy lost
is equal to the energy stored when the material is deformed minus the energy recovered.
Stressed placed in biological structures
is much less then structure can handle.
The amount of mechanical energy stored ..,
is proportional to the area under the stress strain curve. For an elastic material this is the area of triangle.
the modulus of toughness
is the energy needed to completely fracture the material.
the area under the unloading curve
is the energy released by the material. In the elastic range, these areas are equal and no net energy is absorbed.
Elasticity
is the property of complete and immediate recovery from an imposed displacement on release of the load. which the material experiences a permanent residual strain that is not lost on unloading
During loading, the area under the stress-strain curve
is the strain energy per unit volume absorbed by the material.
offset yield strength is that after a specimen has been loaded to
its 0.2 percent offset yield strength and then unloaded it will be 0.2 percent longer than before the test.
As strain is increased,
materials deviate from linear proportionality, until departure point aka- proportional limit. This nonlinearity is associated with stress-induced "plastic" flow . material undergoing rearrangement of internal molecular/ microscopic structure,
microstructural rearrangements associated with plastic flow
not reversed when the load is removed, the proportional limit is often same or close to elastic limit.
The engineering stress strain curve ?
parameters, describing curve of a metal, are: 1) tensile strength (UTS), 2) yield strength or yield point, 3)elongation (E) 4)reduction of area. The first two are strength parameters; the last two indicate ductility.
Yield Point
point where material undergoes permanent deformation s> sy the material no longer return to its original state.
The area up to the yield point is termed the modulus of
resilience, and the total area up to fracture is termed the modulus of toughness. "modulus" units are N-m/m3 or N/m2, which are the same as stress or modulus of elasticity. Resilience" means that up to the point of yielding, the material is unaffected by the applied stress and upon unloading will return to its original shape.
Two types of material failure
single catastrophic stress event, multiple repeated subcritical stress events ( material fatigue)
on a stress - strain curve of viscoelastic material.,
stiffness, yield point, and failure apply as well as elastic and plastic regions. But stiffness is calculated by where is measured in the curve.The mechanical energy stored is not returned resulting in hysteresis or energy lost.
In an viscoelastic material..( tendon, ligaments)
stress- strain relationship are not strictly linear, where the magnitude of stress is dependent upon the rate of loading or how fast loading is applied.
When the specimen fractures,
the engineering strain at break — f — includeS the deformation in the necked and the unnecked region
when the strain exceeds the yield point
the material is deformed irreversibly and some residual strain persists after unloading. The modulus of resilience is the quantity of energy the material can absorb without suffering damage. Similarly, the modulus of toughness is the energy needed to completely fracture the material.
When the applied load is removed from an elastic material ,
the materials will return to its resting length as long as the materials did not reach its yield point.
In tension and compression tests
the relevant area is that perpendicular to the force. S-= F/A0 tensile or compressive stress
In tensile tests, if the deformation is elastic,
the stress-strain relationship is called Hooke's law: s = E e. That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. Elastic moduli measure the stiffness of the material.
the yield stress, denoted σY
the yield stress, denoted σY is the stress needed to induce plastic deformation in the specimen. , the yield stress is often taken to be the stress needed to induce a specified amount of permanent strain, typically 0.2%.
In an elastic material..
there is a linear relationship between stress and strain.That is when the material is deformed by the applied force the amount of deformation is the same for a given amount of stress.
the elastic limit is the value of stress at
which the material experiences a permanent residual strain that is not lost on unloading
