# Proof Resilience

By Aina Parasher|Updated : September 29th, 2022

A body when subjected to external loading, undergoes deformation. During deformation, the body stores up some internal strain energy. The maximum energy that a body can store within the elastic limit is referred to as proof resilience.

In this article, we will understand what is resilience, define proof resilience and the proof resilience formula for a body. We will also understand about modulus of resilience of an object.

## What is Proof Resilience?

Before understanding proof resilience we need to define resilience. A material deforms when subjected to an external load. Due to the property of elasticity, upon the removal of the load, the material will regain its original shape if the load is kept under the elastic limit of the material. During the loading, the material will store strain energy and during unloading, the material will release this stored strain energy. The total strain energy that is stored in the given volume of the material and released during unloading is called Resilience.

The maximum strain energy that can be absorbed by the body within the elastic limit is defined as Proof Resilience. Proof resilience is basically the ability of the body to store strain energy without causing permanent deformation.

## Proof Resilience Formula

To define the proof resilience formula, consider the stress-strain diagram as shown in the figure where the elastic limit coincides with the yield stress of the material.

As we know, proof resilience is the maximum strain energy stored in the volume of the body within the elastic limit. From the stress-strain curve, the proof resilience formula can be given as

Where,

• V = the volume of the body
• E = Young’s modulus

## Modulus of Resilience

Modulus of resilience is defined as the ratio of proof resilience and volume of the body. It can also be defined as the area under the stress-strain curve within the elastic limit. Modulus of resilience is given as.

## Proof Resilience Unit

According to the SI system, the unit of proof resilience is Joule (J) and the SI unit of modulus of resilience can be calculated as-

Modulus of resilience (Ur) = Proof resilience/ Volume

Ur= Joule/ m3

Therefore, the unit of modulus of resilience is J/m3.

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## FAQs on Proof Resilience

• When a body is subjected to an external load, strain energy is stored in the body which is released on unloading. The ability of the body to store strain energy when loaded within the elastic limit is called proof resilience. Proof resilience is defined as the maximum strain energy that a body can absorb when loaded within the elastic limit.

• If the elastic limit coincides with the yield stress of the material then the proof resilience formula can be given as-

U= σy2V/2E

Where, σy = yield stress

V = volume of the body

E = Young’s modulus

• Resilience is the ability of an object to store strain energy when strained within the elastic limit whereas toughness is the ability of an object to absorb energy till the fracture point.

• Modulus of resilience is defined as the proof resilience per unit volume. It can also be defined as the area of the stress-strain curve till the elastic limit. Modulus of resilience is given as

Ury2/2E

Where σy = yield stress

E = Young’s modulus

• Since proof resilience is the maximum strain energy stored in the body when strained within the elastic limit, its unit will be the safe as strain energy, i.e., joule (J). Whereas, the modulus of resilience is proof resilience per unit volume so its unit will be joule per meter cube (J/m3).

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