Bulk Modulus

 When a body is subjected to three mutually perpendicular stresses, of equal intensity, then the ratio of the direct stress to the corresponding volumetric strain is known as bulk modulus. It is usually denoted by K. Mathematically, bulk modulus,

 K = Direct stress / Volumetric strain

 Relation Between Bulk Modulus and Young’s Modulus

The bulk modulus (K) and Young's modulus (E) are related by the following relation,

 E= 3K (1 - 2 µ)

Relation Between Young’s Modulus and Modulus of Rigidity

The Young's modulus (E) and modulus of rigidity (G) are related by the following relation,

 E= 2G (1 + µ)

  Resilience

 When a body is loaded within elastic limit, it changes its dimensions and on the removal of the load, it regains its original dimensions. So long as it remains loaded, it has stored energy in itself. On removing the load, the energy stored is given off as in the case of a spring. This energy, which is absorbed in a body when strained within elastic limit, is known as strain energy. The strain energy is always capable of doing some work.

 The strain energy stored in a body due to external loading, within elastic limit, is known as resilience and the maximum energy which can be stored in a body up to the elastic limit is called proof resilience. The proof resilience per unit volume of a material is known as modulus of resilience.

 It is an important property of a material and gives capacity of the material to bear impact or shocks. Mathematically, strain energy stored in a body due to tensile or compressive load or resilience,

U= (σ² ×V) / 2E

Modulus of resilience = σ² / 2E

where σ = Tensile or compressive stress, V = Volume of the body, and

          = Young's modulus of the material of the body