Modulus of Resilience: Definition and Units

What is Resilience?

Resilience means that the capability of a body to consume energy, when in the elastic limit and they will withstand and come back to their original position from difficult conditions.

Due to resilience property, without having permanent deformation a material can store energy, and as soon as the load is removed and the energy is released and due to this, there is no permanent deformation in the body.

In material for spring action, this property is desired.

What is the modulus of resilience?

The modulus of resilience is the amount of strain energy per unit volume (i.e., strain energy density) that a material can absorb without permanent deformation results. The modulus of resilience is calculated as the area under the stress-strain curve up to the elastic limit.

However, since the elastic limit and the yield point are typically very close, the resilience can be approximated as the area under the stress-strain curve up to the yield point. Since the stress-strain curve is very nearly linear up to the elastic limit, this area is triangular.

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By a material per unit volume, the maximum amount of energy that can be absorbed without creating any permanent deformation in the elastic limit is known as modulus of resilience.

The idea of the modulus of resilience is a must for you if you want to be a good structural engineer and actually resiliences means that the capabilities of a body to consume energy when in the elastic limit the body is deformed.

As ‘μ’ it is normally denoted and the limit is the elasticity limit and also some time is donated as Ur. From material to material, the modulus of resilience varies because, for varying materials, the elasticity limit is not constant.

Unit of Modulus of Resilience

Modulus of Resilience (Ur) is measured in a unit of joule per cubic meter (J·m−3) in the SI system, i.e., elastically deformation energy per surface of the test specimen (merely for the gauge-length part).

modulus of resilience
Modulus of resilience

Ur = Area underneath the stress–strain (σ–ε) curve up to yield = σ × ε

Ur [=] Pa × % = (N·m−2) ·(unitless)

Ur [=] N·m·m−3

Ur [=] J·m−3