# Chapter 3 Elasticity and Strength of Materials - PowerPoint PPT Presentation

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Chapter 3 Elasticity and Strength of Materials. References 1-Physics in biology and Medicine 3 rd e, Paul Davidovits 2- web sites 3- College Physics, 7 th e, Serway. Classification of matter. Matter is normally classified as being in one of three states:

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Chapter 3 Elasticity and Strength of Materials

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## 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

### Classification of matter

• Matter is normally classified as being in one of three states:

• A solid has a definite volume and shape.

• Aliquid 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.

### 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.

### 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.

### Solid Classification

• Solids can be classified as either:

• crystalline: NaCl,

• or amorphous: Glass

### Stress- Strain

• Examine the effect of forces on a body

• 1-stretched,

• compressed,

• bent,

• Twisted

• Elasticityis the property of a body that tends to return the body to its original shape after the force is removed.

### Longitudinal Stretch and Compression

• Stress, S

• Longitudinal Strain, St

• Hook`s Law

### A Spring

energy E stored in the spring is given by

### 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.

### 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

### 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

### 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

### 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.

### 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

• 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

### 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

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

### 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.

### 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).

### Nonomaterial

• Nanotechnology

• is the production of functional materials and structures in the range of 0.1 to 100 nanometers

• 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.

physical or chemical methods

### 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. Size-dependent properties are observed such as quantum confinement in semiconductor particles, and superparamagnetism in magnetic materials, etc..

### 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.

### Some recent publication in dentistry material science

• 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: micrometer

### Assignment

• Solve the following problems

• 1, 3, 5