Short Answer:

Strain is the measure of deformation or change in shape or size of a material when an external force is applied. It shows how much a material stretches, compresses, or twists under the effect of stress. Strain is the ratio of change in length to the original length of the material.

It has no unit because it is a ratio of two lengths (ΔL/L). Strain helps engineers understand how flexible or stiff a material is and how it will behave when subjected to different types of loads such as tension, compression, or shear.

Detailed Explanation :

Strain

Strain is a very important concept in Mechanics of Materials that describes how a material changes its shape or dimension when a load or force is applied. When a material is subjected to stress, it undergoes some deformation. The measure of this deformation with respect to the original size or length of the material is called strain. It represents how much a body is elongated, shortened, or distorted when acted upon by an external force.

Mathematically, strain (ε) is defined as:

where,
ε = Strain (no unit),
ΔL = Change in length (m),
L = Original length (m).

Since strain is a ratio of two lengths, it has no units. It is often expressed as a pure number or sometimes in percentage (%), especially for small deformations. For example, if a rod of 2 meters length is stretched by 0.002 meters, then strain = 0.002/2 = 0.001 or 0.1%.

Types of Strain

Strain can occur in different forms depending on how the force acts on the material. The main types of strain are as follows:

1. Tensile Strain:
   When a material is subjected to a pulling force, it elongates or increases in length. The ratio of increase in length to the original length is called tensile strain. For example, when a steel wire is stretched, it becomes longer, and the strain developed is tensile.
2. Compressive Strain:
   When a material is subjected to a pushing or compressive force, it shortens or decreases in length. The ratio of decrease in length to the original length is called compressive strain. For instance, when a column or spring is compressed, compressive strain is produced.
3. Shear Strain:
   When forces act tangentially or parallel to the surface of a material, one layer of the material slides over the other. The angular deformation between the two layers is known as shear strain. It is measured in radians. Shear strain commonly occurs in bolts, pins, and riveted joints.
4. Volumetric Strain:
   When a body is subjected to uniform stress in all directions (like in pressure vessels or tanks), its volume changes. The ratio of change in volume to the original volume is known as volumetric strain.

Elastic and Plastic Strain

Depending on the nature of deformation, strain is also divided into two categories:

1. Elastic Strain:
   Elastic strain is the temporary deformation that disappears once the applied load is removed. The material returns to its original shape and size. It occurs within the elastic limit of the material. For example, a rubber band stretches under force but returns to its original length when the force is removed.
2. Plastic Strain:
   Plastic strain is the permanent deformation that remains even after the load is removed. It occurs when the applied stress exceeds the elastic limit of the material. In this case, the material cannot regain its original shape completely. This type of strain is important in processes like metal forming, forging, and bending operations.

Importance of Strain in Engineering

Strain helps engineers understand how materials deform under different loading conditions. It provides vital information about material behavior, especially when designing components that must withstand loads without breaking.

• It is used to predict whether a material will remain within its safe elastic limit or undergo permanent deformation.
• In stress-strain analysis, strain helps in determining the modulus of elasticity (E), which indicates the stiffness of a material.
• It assists in comparing materials like steel, aluminum, and plastic based on their flexibility or ductility.
• Strain measurements are essential in strain gauge applications, where sensors detect deformation in machine components and structures.

Relationship Between Stress and Strain

Stress and strain are closely related. Stress is the cause (external force per unit area), while strain is the effect (resulting deformation). Within the elastic limit, both are directly proportional to each other, as stated by Hooke’s Law:

where σ is stress, E is Young’s modulus, and ε is strain. This relationship helps determine the amount of deformation for a given stress and is fundamental in material design.

Practical Example

Consider a steel wire of 2 meters length that elongates by 1 millimeter when subjected to tension.
Change in length (ΔL) = 0.001 m, Original length (L) = 2 m
Then,

This shows that the wire experiences a strain of 0.0005 or 0.05%. This small change in dimension helps engineers evaluate material flexibility and safety under load.

Conclusion:

Strain is the ratio of deformation to the original dimension of a material under applied stress. It indicates how much a material changes in size or shape when subjected to a force. Understanding strain is essential for engineers to design components that can endure loads safely and efficiently without failure. It forms the basis for studying elasticity, plasticity, and overall material behavior under stress.