Table of Contents

## Modulus of Resilience

**Definition of Modulus of Resilience: **The modulus of elasticity is the maximum energy per unit volume that a material can absorb and return to its original position.

If you want to be an excellent structural engineer, then the idea of elastic modulus is a must for you, but in fact, elasticity refers to the ability of an object to consume energy when it is deformed within its elastic limit.

Generally expressed by “μ”, the limit is the elastic limit and is sometimes also expressed by Ur. The elasticity varies from one material to another because the elastic limit is not constant for different materials.

Also Read: Volume of Hollow Cylinder: Its Formula, Surface Area & Examples

## What is Resilience?

Resilience refers to a body’s capacity to absorb energy while it is stretched to its elastic limit, and its capacity to withstand and return to its original position in the face of difficulties.

- Due to its resilience properties, the material will not deform permanently, it can store energy, and once the load is removed and the energy is released, and for this reason, the main body will not deform permanently.
- In materials used for spring action, this characteristic is ideal.

## Calculation of Modulus of Resilience

Let’s learn the equation to calculate this Modulus of Resilience;

As we all know, elasticity is an engineering term that refers to the energy that a material can absorb and return to its original position. Therefore, the area under the elastic portion of the compound’s stress-strain curve and the elastic modulus of a given compound are μ or Ur, respectively;

Where,

*Ur*or*μ*is the modulus of resilience.*σ1*is the yield strain.- And
*E*is young’s modulus

To find out this modulus from the stress-strain diagram, there is also a way;

There is a stress-strain diagram. The elasticity of a material is the area under the linear part of the stress-strain curve. If you combine the stress-strain curve from zero to the elastic limit, you will find the elastic modulus.

**Unit of the Modulus of Resilience**

The unit of elastic modulus is simply the amount of energy absorbed per unit volume of an object. In the SI system, the unit is obviously joules per cubic meter (J/m^{3}).

Please check the stress-strain graph as well.

- The area underneath the stress-strain (σ–ε) curve up to yield = μ = σ × ε.
- μ = Pa × % = …. N·m−2.
- μ = …. N·m·m−3.
- μ = J·m−3.

As a result, the structural engineer or civil engineer must often deal with materials, and the parameter modulus-of-resilience expresses the elasticity limit of a body in a passive way. A body’s load-bearing potential is also reflected.

## Examples of Modulus of Resilience

Calculate the modulus-of-resilience for each of the following materials:

Materials | Yield Strength | |

Mpa | Psi | |

Steel Alloy | 550 | 80,000 |

Aluminum Alloy | 250 | 36,250 |

The formula for calculating this modulus is:

**For Steel;**

= (550 x 10^6 N-m2)2 / (2)207 x 10^9 N /m2

= 7.31 x 10^5 J/m3

**For Aluminum;**

= (250 x 10^6 N /m2)2 / (2) 97 x 10^9 N /m2

= 6.31 x 10^5 J/m3.

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