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Modulus of Resilience | How it is Calculated

Resilience is the property due to which a material can store energy without having permanent deformation and the Modulus of Resilience quantifies this resilience.


More on resilience!


Let us understand what is resilience in common usage; When we say someone is resilient, it means that they will withstand and come back to their original self from difficult conditions. The same applies to materials also.

Resilience is the property due to which a material can store energy without having permanent deformation.

  • This energy is released as soon as the load is removed due to which there is no permanent deformation in the body.

  • This property is desired in material for spring action.

Elasticity


It is the property due to which the material regains its original shape after the load is removed is known as the elasticity and the material is known as the elastic material. The material regains its original shape if the stress is within the elastic limit of the material.

If the stress due to applied load is beyond the elastic limit and then if the load is removed, there will be permanent deformation in the material.


Plasticity


It is the property due to which the material does not regain its original shape after the load is removed is known as the elasticity and the material is known as the plastic material. The material does not regain its original shape, as the stress is not within the elastic limit of the material. If the load is removed, there will be permanent deformation in the material.


Modulus of Resilience

Modulus of Resilience quantifies this resilience. It is defined as the area under the stress-strain curve up to the elastic limit. In other words, it is the strain energy per unit volume for material up to its elastic limit. Here, we are interested only in the elastic limit because that is the energy that can be recovered.


Area under curve/Strain energy per unit volume =1/2 x 𝜎 x 𝜖 = 𝜎y2/2E


In the above formula, 𝜎y is the yield stress of the material.


The unit of modulus of resilience is the same as that of strain energy per unit volume which is Joules/m^3.


Do try out this simple question to check if you have understood true stress and true strain.


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