## Friday, 6 January 2017

We were discussing the concept of stress and strain and also we have discussed the different types of stress and also different types of strain in our previous posts. We have also seen the concept of Hook’s Law in our recent post.

Now we are going further to start our discussion to understand the “Types of modulus of elasticity”, in subject of strength of material, with the help of this post.

### Let us see here the various types of modulus of elasticity

On the basis of types of applied stress and resulting strain, we will have three types of modulus of elasticity as mentioned here
1. Young’s modulus of elasticity
2. Modulus of rigidity
3. Bulk modulus of elasticity

Let us first recall the concept of modulus of elasticity and after that we will see each type of modulus of elasticity in detail.

As we have already discussed that within elastic limit, stress applied over an elastic material will be directionally proportional to the strain produced due to external loading. Mathematically we can say as displayed here.
Let us remove the proportionality sign and therefore we will have to use one constant value in order to remove the proportionality sign.

Where E is basically Modulus of elasticity and we can define modulus of elasticity as the ratio of stress to strain. Modulus of elasticity will have same unit as that for stress because strain is unit less parameter and therefore Modulus of elasticity unit in S.I. system will be N/m2.

### Young’s modulus of elasticity

Young’s modulus of elasticity is basically defined as the ratio of longitudinal stress to longitudinal strain. Young’s modulus of elasticity will be indicated by Y or E.

Young’s modulus of elasticity is basically defined as the property of material which will describe the stiffness of the material and therefore Young’s modulus of elasticity is very important property of a solid material.
Let we have one cylindrical solid bar of length L and cross sectional area is A. Let tensile force F is applied as shown in figure. Change in length of the bar will be Î”L due to external applied tensile force F. Young's modulus of elasticity is calculated above in figure.

### Modulus of rigidity

Modulus of rigidity is also termed as shear modulus and we can define it as ratio of shear stress to shear strain. Modulus of rigidity will be indicated by G.
Modulus of rigidity measures the resistance to the shear deformation
Where,
G, Modulus of rigidity
E, Modulus of elasticity
V, Poisson’s ratio

### Bulk Modulus

Bulk modulus of elasticity is usually referred as the property of material (solid and fluid) in order to determine the compressibility of material or we can say that bulk modulus of elasticity will represent that how much material will be compressed under a certain amount of pressure.

Let we have a solid body with volume V and it is subjected with same stress Ïƒ in three mutually perpendicular directions as shown in figure, body will have uniform changes in three directions and there will not be any distortion in the shape of the body.
Bulk modulus will be defined as the ratio of normal stress to volumetric strain and it will be indicated by K. Reciprocal of Bulk modulus (K) will be termed as compressibility of the material.

### Relationship between Young’s modulus of elasticity (E), modulus of rigidity (G) and Bulk modulus (K)

Do you have any suggestions? Please write in comment box

### Reference:

Strength of material, By R. K. Bansal