Chapter 3
Elasticity and Strength of Materials
References
1-Physics in biology and Medicine 3rd e, Paul Davidovits
2- web sites
3- College Physics, 7th e, Serway
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Classification of matter
• Matter is normally classified as being in one of
three states:
• A solid has a definite volume and shape.
• A liquid has a definite volume but no definite
shape.
• A gas it has neither definite volume nor definite
shape. Because gas can flow, however, it shares
many properties with liquids.
• Often this classification system is extended to
include a fourth state of matter, called a plasma.
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Structure of matter
• All matter consists of some distribution of atoms or molecules.
• In a solid: The atoms, held together by forces that are mainly
electrical, are located at specific positions with respect to one
another and vibrate about those positions.
• At low temperatures
• The vibrating motion is slight and the atoms can be considered
essentially fixed.
• As energy is added to the material,
• The amplitude of the vibrations increases.
A vibrating atom can be viewed as being bound
in its equilibrium position by springs attached to
neighboring atoms. A collection of such atoms
and imaginary springs is shown in Fig.1.
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Structure of matter
• We can picture applied external forces as
compressing these tiny internal springs.
• When the external forces are removed, the solid
tends to return to its original shape and size.
Consequently, a solid is said to have elasticity.
• An understanding of the fundamental properties
of these different states of matter is important in
all the sciences, in engineering, and in medicine.
• Forces put stresses on solids, and stresses can
strain, deform, and break those solids, whether
they are steel beams or bones.
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Solid Classification
• Solids can be classified as either:
• crystalline: NaCl,
• or amorphous: Glass
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Stress- Strain
•
•
•
•
•
•
Examine the effect of forces on a body
1-stretched,
compressed,
bent,
Twisted
Elasticity is the property of a body that tends
to return the body to its original shape after
the force is removed.
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Longitudinal Stretch and
Compression
• Stress, S
• Longitudinal Strain, St
• Hook`s Law
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A Spring
energy E stored in the spring is given by
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Fatigue
• Fatigue is the progressive and localized structural
damage that occurs when a material is subjected to
cyclic loading.
• Fatigue life, Nf, is the number of stress cycles of a
specified character that a specimen sustains before
failure of a specified nature occurs.
• Surface fatigue: Surface fatigue is a process by which
the surface of a material is weakened by cyclic loading.
• Fatigue wear is produced when the wear particles are
detached by cyclic crack growth of microcracks on the
surface. These microcracks are either superficial cracks
or subsurface cracks.
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Bone Fracture: Energy Considerations
• Knowledge of the maximum energy that parts
of the body can safely absorb allows us to
estimate the possibility of injury under various
circumstances.
• Assume that the bone remains elastic until
fracture, the corresponding force is
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Example
• A leg bone 90 cm and an average
• area of about 6 cm2
• Y=14×1010 dyn/cm2
• This is the amount of energy in the impact of a
70-kg person jumping from a height of 56 cm
(1.8 ft), given by the product mgh.
•
•
E= 70x10xH=384 J
H=384/700=0.56 m= 0.56 cm
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Impulsive Forces
• In a sudden collision, a large force is exerted for
a short period of time on the colliding object.
• For example, if the duration of
a collision is 6×10−3 sec and the
• change in momentum is 2 kg m/sec, the
average force that acted during the collision is
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Fracture Due to a fall: Impulsive
Force Considerations
• The magnitude of the force that causes the damage
is computed
• the duration of the collision Dt is difficult to
determine precisely
• If the colliding objects are hard, very short~ few
milliseconds
• If the objects is soft and yields during the collision,
the duration of the collision is lengthened, and as a
result the impulsive force is reduced.
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Example
• When a person falls from a height h, his/her
velocity on impact with the ground, neglecting
air friction
• W=mg
• After the impact the body is at rest : mvf = 0
• Measuring time is a problem
• Vertical fall
Dt=10-2 sec
• bends his/her knees or falls on a soft surface
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• Table 3.1, the force per unit area that may
cause a bone fracture is 109 dyn/cm2
• person falls flat on his/her heels, the area of
impact may be about 2 cm2.
Body of mass of 70 kg, Dt = 10−2 sec
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Airbags: Inflating Collision
Protection Devices
• The impact force may also be calculated from
the distance the center of mass of the body
travels during the collision under the action of
the impulsive force.
30 cm
v
Decelerating force, F
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For A =1000 cm2
• At an impact velocity of 70 km/h
• F= 4.45×106 dyn
• Stress= 4.45×103 dyn/cm2 < The estimated
strength of body tissue.
• At a 105-km
• F= 1010 dyn
• Stress= 107 dyn/cm2. probably injure the
passenger
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Whiplash Injury
• the impact is sudden, as in a rear-end collision,
• the body is accelerated in the
forward direction by the back
of the seat,
the unsupported neck is then suddenly yanked
back at full speed.
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Falling from Great Height
•
•
•
•
•
Falling on a hard surface
Cause injury
Energy=mgh=1/2 mv2
Falling on a soft surface
Example:
decelerating impact force acts over a distance
of about 1 m, the average value of this force
remains below the magnitude for serious
injury even at the terminal falling velocity of
62.5 m/sec (140 mph).
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Nonomaterial
• Nanotechnology
• is the production of functional materials and
structures in the range of 0.1 to 100 nanometers
physical or chemical methods
• one hydrogen atom is 0.1 to 0.2 nm and of a
small bacterium about 1,000 nm
• Nanotechnologies are predicted to revolutionize:
• (a) the control over materials properties at ultrafine
scales; and
• (b) the sensitivity of tools and devices applied in
various scientific and technological fields.
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Nanomaterials
• It studies materials with morphological
features on the nanoscale, and especially
those that have special properties stemming
from their nanoscale dimensions.
• A bulk material should have constant physical
properties regardless of its size,
• At the nanoscale this is often not the case. Sizedependent properties are observed such as quantum
confinement in semiconductor particles, and
superparamagnetism in magnetic materials, etc..
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Example
• For example,
• the bending of bulk copper (wire, ribbon, etc.)
occurs with movement of copper atoms/clusters
at about the 50 nm scale.
• Copper nanoparticles smaller than 50 nm are
considered super hard materials that do not
exhibit the same malleability and ductility as bulk
copper.
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Some recent publication in
dentistry material science
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April 13, 2015
• Figure 1. Schematics and
transmission electron
microscopic images of
composites studied. A.
Composite with nanometric
particles (× 60,000
magnification). B. Composite
with nanocluster particles
(×300,000 magnification). C.
Composite with hybrid fillers
(×300,000 magnification).
• nm: Nanometers. APS:
Average particle size. μm:
25
micrometer
Assignment
• Solve the following problems
• 1, 3, 5
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