Table of Contents

# What Is modulus of resilience and Its Units -Strength Of Material

### Definition Of resilience :

Resilience is the ability of a material to withstand elastic deformation without deforming plastically. In other words, resilience involves the stretching of atomic bonds prior to the breaking of the bonds. The maximum amount of volume that a material will elastically deform before becoming permanently deformed is known as the modulus of resilience.

*Modulus Of resilience :*

*Modulus Of resilience :*

he 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 resulting. 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.

**Modulus of resilience = Proof resilience / Unit volume of the body**

- ie. The stain Energy stored below the Elastic Limit Called resilience.

- It can be calculated by integrating the stress-strain curve from zero to the elastic limit.

**U***r* = ∫ *E εx dεx*

- The
*capacity*of a*structure to withstand an impact*load*without*being*permanently deformed*depends upon the resilience of the material.

In uniaxial tension, under the assumptions of linear elasticity Modulus of resilience **Interm’s of Stress and Youngs modulus**

**U**r = **σ**y X **σ**y** / **2E

Where,

**U***r* – Modulus of resilience

** σ**y – Yeild Stress

E- Youngs Modulus

**Interms of Area Using stress and strain**

*U*r = *Area underneath the stress–strain (σ–ε) curve* = ** 1/2′ **X

**σ**X

**ε**

Where,

** σ**y – Stress at the Elastic limit

**ε**– Strain at the Elastic limit

*Modulus of resilience Example : *

All materials have different moduli of resilience. Rubber is an example of a material that has an extremely high modulus of resilience. Ceramics typically have a very low modulus of resilience. In terms of metals, brass has a relatively high modulus of resilience, while a metal such as cast iron has a relatively low modulus of resilience.

**Modulus of resilience Units :**

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

Like the unit of tensile toughness (UT), the unit of resilience can be easily calculated by using area underneath the stress–strain (σ–ε) curve, which gives resilience value, as given below:

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**