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# Elasticity

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## Introduction

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Elasticity is a property of matter that explains the deformation of materials. Whenever a force is exerted on a solid it undergoes deformation. When an external force is applied to a rigid body there will be a change in its length, volume, shape. The change in parameters depends upon the ratio of applied stress to the resulting strain. When the external forces are removed from the body it tends to regain its original shape and size. Such a property of a material by virtue of which the body tends to regain its original shape, size as a result of removal of external forces is known as the elasticity.

## What is Elasticity?

Whenever we discuss the mechanical properties of materials, the important concept to be studied is the elasticity of particular material (elastic properties of materials)  that will explain the durability of the material. The property of matter by virtue of which the materials retain their original shape and size after removing deforming forces is known as elasticity. The elasticity is mainly due to the intermolecular forces between the atoms or the molecules of the body. For elastic materials examples, we have, rubber, spring, etc…

The materials that exhibit elasticity or get deformed are known as the elastic materials and the bodies that will not get deformed are known as rigid bodies. In rigid bodies, the separation between its constituent particles will not change. In nature, they are not perfectly elastic and perfectly rigid. Whenever any deformation takes place in elastic bodies its energy will be stored in the form of elastic potential energy.

In nature, there are no perfectly elastic or inelastic bodies. But there are elastic and partially elastic bodies. Perfectly elastic bodies refer to the object which regains its original shape and size after removing deforming forces, practically it is impossible to have perfectly elastic bodies, all the objects will eventually lose their original shape and size after applying deforming forces.

### Elasticity Definition

Now let us have a look at what is elasticity in physics, so elasticity is a property of matter by virtue of which the materials retain their original shape and size after removing deforming forces, this is the elasticity definition of physics.

Now, let us move from the consideration of forces that affect the motion of an object to those that affect an object’s shape. A change in shape due to the application of a force is a deformation is also known as the elastic force. Even very small forces will cause some deformation.

For small deformations, there are two important characteristics that are to be observed:

1. The object returns to its original shape after the removal of force i.e., the deformation is elastic for small deformations.

2. The size of the deformation is proportional to the applied force i.e., for small deformations, Hooke’s law is obeyed.

Whenever we study the elastic properties or elasticity physics, the first and foremost important concept to be understood is Hooke’s law. Hooke’s law gives the relationship between stress applied and the resulting strain. Hooke’s law states that the ratio of the stress to resulting strain will always be constant or the stress applied will be directly proportional to the resulting strain. Mathematically we write,

$\Rightarrow \frac{Stress}{Strain}=Constant$

We can say Hooke’s law is the elasticity formula physics. The constant of proportionality is known as the modulus of elasticity.

### What is Stress?

When the body is deformed by the application of external forces, forces within the body are brought into action. Elastic bodies regain their original shape by virtue of internal restoring forces. The internal forces and external forces are always opposite in direction.  If a force F is applied uniformly all over a surface of area A then the stress is defined as the force per unit area. SI unit of stress is N/m2

Therefore, mathematically we write:

$\Rightarrow Stress=\frac{Force}{Area}$

Depending upon the type of forces there are three types of stresses, given by:

1. Longitudinal Stress

2. Volume stress or Bulk stress

3. Shear stress

### What is a Strain?

A body subjected to stress gets deformed. The fractional change in the dimension of a body is produced by the external stress acting on is called strain. The ratio of change of any dimension to its original dimension is called the strain. Since strain is the ratio of two identical dimensions, therefore strain is a unitless quantity.

Mathematically, the strain is given by:

$\Rightarrow Strain=\frac{Changeindimension}{Originaldimension}$

The strain is again classified into three types:

1. Longitudinal Strain

2. Volume Strain or Bulk Strain

3. Shear Strain

### Modulus of Elasticity

Now, the modulus of elasticity of any material is the ratio of stress applied to the material to strain in the material. It is obtained from Hooke’s law. Depending upon the type of stress being applied and the resulting strain there are three types of modulus of elasticity, they are:

1. Young’s Modulus: It is defined as- the ratio of longitudinal stress to longitudinal strain, is denoted by Y.

2. Bulk Modulus: It is defined as- the ratio of volumetric stress (or volume stress) to strain, and is denoted by B.

3. Shear Modulus: It is defined as- the ratio of shear stress to shear strain, and is denoted by 𝜂.

### Did You Know

Certain fabrics are manufactured in such a way that they are elastic in nature. Spandex is a synthetic material that is the best example of fabrics exhibiting elasticity. Spandex is extremely stretchable. Spandex is used to make swimming suits and clothes for cyclists. But every material has its own limit for stretching beyond which it can not be stretched further is known as the elastic limit. A fun fact about elasticity is that rubber can be stretched to three times its original size.