Stress and Strain - Definition, Curve, Hooke's Law, SI Units, Types, FAQs

Stress and strain are fundamental concepts in physics and engineering that describe how materials respond to external forces. Stress refers to the internal force per unit area within a material, caused by an applied load, while strain is the deformation or displacement that occurs as a result of this stress. These principles aren't just theoretical but have practical applications in everyday life. For example, when we apply pressure on a rubber band (stress), it stretches (strain). Similarly, the way a bridge or building bends or flexes under the weight of vehicles or wind is a real-life demonstration of stress and strain. Understanding these concepts helps engineers design safe structures and products that can withstand various forces without breaking or deforming. Even in our bodies, bones and muscles experience stress and strain during physical activities like running or lifting, making these ideas crucial in biomechanics and medical science.

Elastic or Deforming Force

It is the applied force onto a body by which its shape or size changes over time, the change can be in length, breadth volume or change on all three of these. That is there will be a change in the normal shape of the molecule implying that there is a change in the arrangement of molecules.

Elasticity

It is the special ability of a body to regain its initial original configuration on the removal of the deforming force. Those materials showing the elastic property are called elastic materials. The more elastic the material is faster it can turn back into its original state.

Examples of elastic materials are quartz fibre. phosphor bronze, etc

Plasticity

It is the inability of a body to regain its original status on the removal of the deforming forces, the objects or materials that obey the plasticity property are called plastic materials

Examples of materials that show plasticity or plastic materials are - bakelite, plastic etc.

What is Stress

The restoring force or deforming force experienced per unit area on a body is called stress. It has the dimension of force per area or the same dimension as that of pressure.

Stress = Force/Area

SI unit of stress is Nm-2

Types of Stress

Usually, stress is classified into four types of stress depending on the way in which the stress is applied: they are Normal stress, tensile stress, compressive stress, and Tangential stress.

1. Normal Stress

Normal stress occurs when the elastic restoring force or deforming force operates perpendicular to the region. The following are some of the most common types of normal stress.

A. Tensile Stress

The stress developed inside the body is called tensile stress when the length of the body increases In the direction of the applied force.

Here in the below image, you can see that when the force is applied in a particular direction the length of the body increases in the same direction as that of the applied force.

Image of tensile stress(source self-made MS Paint 3D)

B. Compressive Stress

The stress developed inside the body is called compressive stress when the length of the body decreases in the direction of the force applied.

Here in the figure below you can see that the length of the body decreases in the direction of the applied force.

Image of compressive stress(source self-made MS Paint 3D)

2. Tangential or Shearing Stress

Tangential stress occurs when an elastic restoring force or deforming force operates parallel to the surface area. Here in the figure below you can see that the force is applied along a surface and it is called tangential because the force is not perpendicularly applied rather it is applied tangentially to the surface.

Image of shearing or tangential stress

What is Strain

The strain has several meanings in literature here we are going to look at what is strain in physics. Strain definition can be made as it is a fraction which compares the change in the configuration of the body to the original configuration or the initial configuration of the body. Since the numerator and denominator of the term have the same dimension they cancel out each other and hence strain in a dimensionless quantity.

Strain =Change in configuration original configuration

There are different types of strains discussed below

Depending on the surface of the applied force and the change in the shape of the objects, strains can be classified as three – Longitudinal strain, volumetric strain, and shearing strain.

1. Longitudinal Strain

It is the relation between the change in length and the original length of the body where force is applied. This type of strain is calculated in the case where the deforming force is acting perpendicular to the surface

Longitudinal Strain =Change in length/Original length

2. Volumetric Strain

It has the same definition as that of the strain but here the force acting on the body from all directions not only causes the change in length but totally the entire volume is changed. So it can be written as the ratio of change in volume of the body to the original volume.

Volumetric Strain = Change in volume/Original volume

3. Shearing Strain

A tangential force causes a plane perpendicular to the fixed surface of the cubical body to turn via an angle (in radians).

Image of shearing strain

Stress vs strain curve or stress-strain diagram or stress-strain curve for brittle material

Stress and strain are represented here in the curve

Hooke's Law

In the case of small deformations that is when the applied force is small but it should be enough to cause deformations, in such conditions the stress acting on the body is directly proportional to the strain, it can be seen in the above stress and strain curve. It is also called stress-strain theory.

Stress α Strain

Stress = k x Strain

Where, K is the proportionality constant, and is known as the modulus of elasticity, in the above stress-strain curve diagram, the region that obeys Hooke’s law is called as Hooke” 's law curve.

Elastic Moduli:- Modulus of elasticity - According to Hooke's law, within clastic limit stress is directly proportional to the strain, which can be seen in the stress-strain graph above. Which implies

Stress α Strain

Stress = E x Strain

Stress/Strain=E=constant

Where E is known as the modulus of elasticity or elastic moduli, the ratio of stress and strain is known as the modulus of elasticity, there are different kinds of modulus of elasticity according to the type of stress and strain which is discussed below

Types of Modulus of Elasticity

1. Young's Modulus of Elasticity (Y)

When the force acted is normal to the surface the stress and strain will be normal and hence its proportionality constant is discussed here as Young’s modulus

Y = Normal stress/Longitudinal strain

2. Bulk modulus of elasticity (B)

The bulk modulus is the ratio of normal stress to the volumetric strain.

B = Normal stress/Volumetric strain

Its Unit is - Nm or Pascal

Compressibility (A) - Reciprocal of bulk modulus of elasticity (B)

3. Modulus of Rigidity or shear modulus of elasticity (G)

When the deforming force is acting shear to the surface or tangential surface the stress and strain developed will be shear strain and tangential stress. The proportionality constant in this case is called the rigidity modulus or the shear modulus.

G = Tangential stress/Shearing strain

Recommended Topic Video

Solved Examples Based on Stress and Strain

Example 1: The elastic limit of brass is 379MPa.What should be the minimum diameter (in mm) of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

1) 1

2) 1.16

3) 0.9

4) 1.36

Solution:

As we know that

$\begin{aligned} & \text { stress }=\frac{F}{A} \\ & \Rightarrow 379 \times 10^6=\frac{400 \times 4}{\pi d^2} \\ & \Rightarrow d^2=1.35 \times 10^{-6} \\ & \Rightarrow d=1.16 \times 10^{-3} \mathrm{~m}\end{aligned}$

Hence, the answer is the option (2).

Example 2: A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that $g=3.1 \pi \mathrm{ms}^{-2}$ what will be the tensile stress (Nm^-2) that would be developed in the wire?

1) 4800000

2) 5200000

3) 3100000

4) 6200000

Solution:
$
\begin{aligned}
& \text { Stress }=\frac{\text { force }}{\text { Area }}=\frac{F}{A} \\
& \text { wherein } \\
& \begin{array}{l}
F=\text { applied force } \\
A=\text { area } \\
r=2 \mathrm{~mm} \\
m=4 \mathrm{~kg}, g=3.1 \pi \mathrm{ms}^{-2}
\end{array}
\end{aligned}
$
So, $F=m g$

$
\begin{aligned}
& \text { Stress }=\frac{F}{A}=\frac{m g}{\pi r^2}=\frac{m \pi \times 3.1}{\pi(4) \times 10^{-6}} \\
& \text { Stress }=\frac{4 \times 3.1 \times \pi}{\pi \times 10^{-6} \times 4}=3.1 \times 10^6 \mathrm{~N} / \mathrm{m}^2
\end{aligned}
$

Hence, the answer is the option (3).

Example 3: The unit of stress is the same as that of

1) Force

2) Torque

3) Surface tension

4) Pressure

Solution:

Both stress and pressure are defined as the force acting per unit area. Hence, both have the same unit i.e.

Hence, the answer is the option (4).

Example 4: Which of the following quantities will change due to tensile stress?

1) Shape

2) Volume

3) Both shape and volume

4) Neither shape nor volume

Solution:

Longitudinal Stress (Tensile Stress)

Increase in length under a deforming force.

wherein

Due to tensile stress, Both shapes as well as volume remain unchanged.

Hence, the answer is the option (4).

Example 5: When a bar is subjected to an increase in temperature and its deformation is prevented, the stress induced in the bar is

1) Tensile

2) Compressive

3) Spear

4) None of the above

Solution:

Longitudinal Stress (Compressive Stress)

Decrease in length under a deforming force.

wherein

As temperature increases will cause an increase in length hence to prevent this we must apply compressive stress.

Hence, the answer is the option (2).

Summary

Stress refers to the force per unit area acting on a material, while strain is the resulting deformation or change in shape. These concepts are fundamental in understanding how materials respond to forces, with examples like tensile, compressive, and shearing stresses. Elasticity allows materials to return to their original form after the removal of force, while plasticity causes permanent deformation. Hooke's Law explains that, within the elastic limit, stress is proportional to strain, with a modulus of elasticity quantifying this relationship.