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

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The basic difference between young’s modulus,bulk modulus and shear modulus is that Young’s modulus is the ratio of tensile stress to tensile strain,bulk modulus is the ratio of volumetric stress to volumetric strain and shear modulus is the ratio of shear stress to shear strain.

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

Aluminium707030
Bone1580
Copper11014044
Diamond1120 540 450
 Glass 553123
Steel20016084
Tungsten390200150
Water02.20
Lead157.75.6

 

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