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## Young’s modulus

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

### 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

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

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

Material |
Young’s modulus 10 |
Bulk modulus 10 |
Shear modulus 10 |

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 |