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Difference between young’s modulus,bulk modulus and shear modulus

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Young’s modulus

The ratio of tensile stress to tensile  strain is called young’s modulus.

Young’s modulus formula

young's modulus formula

Bulk modulus

For three dimensional deformation,when volume is involved,then the ratio of applied stress to volumetric strain is called Bulk modulus.Mathematically it is expressed as:

Bulk modulus formula

bulk modulus formula

Where ΔV is the change in original volume V.

Shear modulus

The ratio of shear stress and shear strain is called shear modulus.Mathematically it is expressed as:

Shear modulus formula

shear modulus formula

Elastic constants for some of the materials are given in table:

Material

Young’s modulus

109Nm-2

Bulk modulus

109Nm-2

Shear modulus

109Nm-2

Aluminium 70 70 30
Bone 15 80
Copper 110 140 44
Diamond 1120  540  450
 Glass  55 31 23
Steel 200 160 84
Tungsten 390 200 150
Water 0 2.2 0
Lead 15 7.7 5.6

 

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