Elastic Moduli: Overview, Questions, Preparation

According to this theory, the stress due to applied pressure on the body will be directly proportional to the strain developed. It can be represented as:

Stress∝Strain

Stress=E×Strain

Where E = Elastic Moduli

Mathematical Representation: F = kx

Where,

F = applied force

K = spring constant

X = expansion/contraction of the length

Elastic moduli are defined as the ratio of stress ( σ=F/A  ) to strain ( ε  ) under specific conditions, all within the elastic limit. Some common types of elastic moduli are mentioned below:

Young's Modulus/Modulus of Elasticity (Y)

It is used to determine how much elasticity a stretched body can have. General Formula:

E = Stress/Strain

SI Unit = Pascal or N/m^2

Shear Modulus/Modulus of Rigidity (G)

It is used to measure a material's resistance. General Formula:

G = Shear Stress/Shear Strain

SI Unit = Pascal or N/m^2

Bulk Modulus (K)

It is used to determine the resistance under hydrostatic pressure. General Formula:

K =-PΔV/V=PV-ΔV

Where,

ΔP is change in the pressure

VΔV​ is the fractional volume change.

Poisson's Ratio ( σ  )

It is used for calculating the ratio of lateral strain to longitudinal strain. General Formula:

σ=- Lateral strain/Longitudinal strain 

It is a dimensionless quantity

All the above mentioned elastic moduli are interconnected to each other and are represented by:

Y=2G(1+ν)

Y=3K(1−2ν)

Where

Y = Young’s Modulus

G = Shear Modulus

K = Bulk Modulus

V = Poisson’s ratio

Elastic moduli can also depend on various factors that can determine the impact of stress and strain on the material, such as:

• Material Composition: A Strong bond means higher moduli. Similarly, a weak bond means lower moduli.
• Temperature: Moduli is inversely proportional to the temperature. Higher temperature can lead to low elastic moduli.
• Presence of Impurities: These can increase or decrease the moduli depending on their interaction with the material.
• Density of the Material: Denser materials have stronger bonds which can lead to more elastic moduli.

Some real world applications of Elastic Moduli important for general information are given as follows:

• Construction and Engineering: Choose material with appropriate elastic modulus to withstand pressure.
• Aerospace Industry: Use materials to design light weight aircrafts and vehicles.
• Medical Science: Match the elastic properties of bones and tissues to design the equipment accordingly (eg: braces).
• Rock Mechanics: Used to check behavior of rocks under high pressure to help study the nature of the earth.
• Fluid Mechanics: Used to observe the behavior of fluids under pressure and conduct scientific research.

Here are some of the major drawback on elastic modulus which the aspirants need to be aware of:

• Valid only within the elastic limit.
• Assumes linear behavior between stress and strain (based on Hooke’s Law).
• Can change according to the temperature.
• Can’t be used in highly complex situations.
• Unable to predict failures in the model.
• Can be affected by impurities.

For Revision Notes H2

 

Units and Measurements Class 11 Notes	Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes	Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane	Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes	Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes	Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes	Oscillations Class 11 Notes
Gravitation Class 11 Notes	Waves Class 11 Notes

 

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