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# Elastic Behaviour of Materials

## Introduction

Every matter in the universe is composed of tiny particles called molecules. They attract each other with some attractive force. There exists an intermolecular force of attraction between molecules. Based on the force of attraction between the molecules, matters are classified into five categories. They are solid, liquid, gas, plasma, and Bose-Einstein. Solids are the matter in which the distance between the molecules is very small and they are tightly bound to each other. Liquids are matter having molecules at a small distance and they bound less tightly than solids.

## What is Elasticity?

When a force is applied to a body it gets deformed. If the body gets back its original shape after the removal of force from the body then the force is called elastic force. As it deforms the dimension of the body it is called a deforming force. This phenomenon of the body is called elasticity. When s rubber is stretched by applying force the length and thickness of the rubber change. After removing the force it gets to its original size. This property is called Elasticity.

## Elastic Properties of Materials

Strength is the ability of the solid to remain unchanged due to the stress applied to it. It also has resistance to change. If the resistance of the body to the deforming force is less, then it gets deformed easily.

When a force is applied to a body, the shape of the body changes. If it regains its shape after the removal of force it is called elasticity.

If the body cannot return to its original shape after the removal of deforming force, it is called plasticity.

The ability of the solid material to stretch into a thin sheet, wire, or plate is called ductility.

Hardness is the material’s ability to avoid scratching, cutting, and penetrating.

As the intermolecular distance between the molecules of the solid material is small the force between them is very strong.

The molecules in the solid materials are placed very close to each other. As the distance between them is small, solid materials are incompressible.

Due to the small separation of the distance, they are hard and rigid.

Solid can pass current through them.

Chemical changes make changes in the composition of matter.

Toughness is the combined form of plasticity and strength.

## Hooke's Law

Inside the elastic limit, the strain formed in the material is directly proportional to the stress applied.

$$\mathrm{stress\propto strain}$$

Which is known as Hooke’s law.

**Stress** − The force applied to the body which changes the dimensions of the body is called
stress.

$$\mathrm{stress=\frac{force}{area}}$$

The unit of stress is $\mathrm{Nm^{-2}}$.

**Strain**− When stress is applied to a body it gets deformed. The ratio between the dimensional
change to its original dimension is known as strain.

$$\mathrm{strain=\frac{change\:in\:dimension}{original\:dimension}}$$

It has no unit.

## Modulus of Elasticity

Modulus of elasticity gives the relation between stress and strain. The ratio between the stress applied to the material and the strain formed due to the applied stress is constant. This constant is called the modulus of elasticity.

$$\mathrm{\frac{stress}{strain}=k}$$

k - modulus of elasticity or elastic constant.

There are three types of modulus of elasticity. They are Young’s modulus, Rigidity modulus, and bulk modulus.

### Young’s Modulus

Modulus of elasticity gives the relation between stress and strain. Young’s modulus is the ratio between longitudinal stress to linear strain. When a force is applied to the object normal to it that force acts per unit area as longitudinal stress. Due to this stress, there is a change in the length of the object. The ratio between the change in the length and the original length is called linear strain.

$$\mathrm{Young's\:Modulus(E)=\frac{longitudinal\:stress}{linear\:strain}}$$

$$\mathrm{E=\frac{F/a}{\Delta L/L}}$$

$$\mathrm{E=\frac{FL}{a\Delta L}}$$

### Bulk Modulus

Bulk modulus is the ratio between compressive stress and the volume strain. Compressive stress is the stress applied to the whole body. Volume strain is the ratio between the change in volume and the original volume.

$$\mathrm{Bulk\:Modulus(K)=\frac{compressive\:stress}{volume\:strain}}$$

$$\mathrm{K=\frac{F/a}{\Delta v/v}}$$

$$\mathrm{K=\frac{Fv}{a\Delta v}}$$

### Rigidity Modulus

It is the ratio between the tangential stress and the shearing strain. The stress applied tangent to the object is tangential stress. The ratio between the change in angle and the original angle is shearing strain.

$$\mathrm{Rigidity\:Modulus(K)=\frac{tangetial\:stress}{shearing\:strain}}$$

$$\mathrm{n=\frac{F/a}{\Delta \theta }}$$

## Stress-Strain Curve

The graphical representation of strain to stress is given below.

In this curve,

*OA*represents the region in which the strain is directly proportional to stress.As stress is increased to a high magnitude the strain increases rapidly and the stress-strain relation ceases to hold. That point A is the elastic limit.

After point B the strain increases and it is the strain-softening point.

From point c onwards the material gets hardened

D is the breaking point.

## Applications

Carrying heavy loads is done with strong materials. The Load carried by cranes and lifts is very high. So the ropes and cables used for suspensions should be made of strong material. So materials having higher young’s modulus are used for the ropes and cables.

Knowing the strength of the solid materials is possible by the material’s elastic behavior. By the knowledge of this property, materials that best suit the construction of pillars, and columns for building are selected.

Knowledge about the elastic behavior of the materials is very much important in engineering.

The principle of elasticity is also useful in measuring the height of mountains.

Bridges should not get deformed due to heavy traffic or hurricanes. That is done by knowing the elastic property of solids.

The metallic parts of the machines get deformed if the force exceeds the elastic limit. Proper choosing of material is done by this property.

## Conclusion

The different states of matter are explained in this article. In this tutorial, elasticity is also discussed. The elastic properties of the material are also discussed. Hooke’s law, modulus of elasticity, and different types of elasticity are also discussed. The relation between stress and strain, its graphical representation, and explanation was given above. The applications of the materials are also discussed

## FAQs

**Q1. What are the factors affecting the elasticity?**

Ans. Many factors affect the property of elasticity. They are stress, temperature, nature of the crystal, annealing, and impurities.

**Q2. What is Poisson's ratio?**

Ans. The ratio between the lateral strain and longitudinal strain is constant. That constant is called Poisson’s ratio.

$$\mathrm{poisson\:Ratio=\frac{lateral\:strain}{longitudinal\:strain}}$$

**Q3. Does the modulus of elasticity vary with temperature?**

Ans. If the temperature of the material increases the lattice vibrations of the material increase. This decreases the modulus of elasticity of the material.

**Q4. What is an elastic limit?**

Ans. If stress is applied to a body it gets deformed. After the removal of that stress, it returns to its original position. There is maximum stress before which the body can regain its dimension known as the elastic limit. Beyond this limit, the body cannot regain its original dimensions.

**Q5. Which materials are used in heavy machines? why?**

Ans. Steel and brass materials are preferred to use in heavy machines. Because their young’s modulus is very high and needs large force for deformation.