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QUESTION: 1

The independent elastic constants for homogeneous and isotropic material are

Solution:

Only two independent elastic constant are required to express the stress-strain relation for a linearly elastic, isotropic material. We can find third elastic constant and Poisson’s ratio for the material.

QUESTION: 2

For a linearly elastic, isotropic and homogeneous material, the number of elastic constants required to relate stress to strain is

Solution:

QUESTION: 3

If the Young’s modulus E is equal to bulk modulus K, then the value of Poisson’s ratio is

Solution:

E = 3 K ( 1 - 2 v)

(∴ E = K)

QUESTION: 4

What will be the value of the Poisson’s ratio if the Youngs modulus E is equal to the bulk modulus K?

Solution:

K = E / 3(1 – 2μ)

Since K = E

So (1-2μ) = 1/3

Therefore, μ = 1/3.

QUESTION: 5

A 50 cm long x 20 cm diameter cylinder of brass was subjected to a tensile load of 0.1 MN. The resulting increase in length and decrease in diameter were noted 1 mm and 0.1 mm respectively. Then the brass has a Poisson’s ratio equal to

Solution:

QUESTION: 6

Consider a bar of length L, breadth B and thickness t subjeced to an axial pull or tension P. The resulting volumetric strain will be equal to

Solution:

where v is the Poisson’s ratio and ∈ is the longitudinal strain.

QUESTION: 7

If E, G and K denote the Young’s modulus, modulus of rigidity and bulk modulus for an elastic material, then which one of the following can be possibly true?

Solution:

Most of the elastic material,

v = 0.25 to 0.33

so, for v = 0.25, E = K x 3(1 - 0.5 ) = 1.5 K

and v = 0.33,

(Possible relation)

QUESTION: 8

A spherical ball of 0.5 x 10^{3} mm^{3} volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal to

Solution:

Bulk modulus

QUESTION: 9

For an isotropic, homogeneous and elastic material obeying Hooke’s law, number of independent elastic constants are

Solution:

QUESTION: 10

The number of elastic constants for a completely anisotropic elastic material are

Solution:

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