What is Strain in Mechanics – Strength of Material

When external force is applied to a rigid body. It changes its size and shape due to internal mechanical stress acting on it. This change in length is represented by strain. This article covers what is strain in mechanics? Types of strain and how Mechanical Strain is calculated?

Strain in mechanics measures the deformation in a material when mechanical stress is applied to it. Mathematically mechanical strain is equal to the ratio of change in length to the original length.

This image shows the strain produced in a rectangular bar when external force is applied.
Mechanical Strain

Strain is a dimensionless quantity and It is denoted by “ε”. Lets try to understand strain in context to external force and stress applied.

Example of strain in Mechanical Engineering

A rubber band changes its length and cross section area when it is pulled with external force. This change in length and cross section area can be represented by mechanical strain.

When rubber band is pulled with an external force. It changes its length and cross section area.

In the above example, mechanical strain in the rubber band depends on following factors:

  1. Stress Acting in the Material: Higher the applied external force, Higher will be the stress produced inside the material. As a result higher will be the strain produced in the material. In this way strain in mechanical engineering is directly proportional to stress acting on a body. Without stress there will be no strain. No matter if external force is acting on the body. 
  2. Cross Sectional Area: Higher the cross section area, lower will be the produced stress. As a result lower will be the strain. Therefore strain in mechanics is inversely proportional to cross section area of the body.
  3. Resting Force Exhibited by the Body: Resting force exhibited by a body depends on its material. For example, Steel will exhibit higher resistance compared to rubber material. Therefore strain in mechanics is directly proportional to a mechanical properties of a material.

Types of Strain in Mechanical Engineering

When an external force is applied to a body. There is a change in part length due to stress produced inside the material. This change in length can be in longitudinal or lateral direction. Based on direction of change in length. Mechanical Strain can be classified into following types.

  1. Normal Strain
    • Lateral Strain
    • Longitudinal Strain
  2. Shear Strain
  3. Volumetric Strain
1. Normal Strain

Normal Strain in mechanics is the strain produced inside a body when an external force perpendicular to cross sectional area is applied. This external force results in the change in part length in the direction and perpendicular to the direction of applied load. 

Change in length in the direction and perpendicular to the direction of applied load is represented by longitudinal and Lateral strain respectively. Change in length in the direction perpendicular to applied force occurs due to Poisson Effect. This change in the length can be calculated using Poisson’s Ratio

Normal Strain in mechanics is the strain produced inside a body. When a force perpendicular to cross sectional area is applied.
Lateral and Longitudinal Strain in Mechanical Engineering
1.1) Lateral Strain
Lateral Strain is the Ratio of change in length to the original length in the direction perpendicular to the applied force.
Lateral-Strain Calculation Formula

Mathematically lateral strain is equal to the ratio of change in length to the original length in the direction perpendicular to the applied force.

1.2) Longitudinal Strain
Longitudinal Strain is the Ratio of change in length to the original length in the direction of applied force.
Longitudinal Strain Calculation Formula

Mathematically Longitudinal strain is equal to the ratio of change in length to the original length in the direction of applied force.

2. Shear Strain

Shear Strain is produced in a material when two equal and opposite non-aligned forces are applied to a body. 

Change in the tangential angle in the direction of shear force acting on a body is known as shear strain.

Mathematically shear strain is equal to the Change in the tangential angle in the direction of applied shear force. It’s value is measured in radians.

Shear Strain (γ) = Tan θ

3. Volumetric Strain

Volumetric strain is a type of mechanical strain that is produced inside a body when external force is applied from all directions of a body.

Volumetric strain is produced inside a body when external force is applied in all directions of a body.

For example, in a gas tank, gas produces volumetric strain inside the tank. Mathematically volumetric strain is the ratio of change in volume to the original volume.

True Strain vs Engineering Strain

When an external tensile force is applied to a metal rod. It’s diameter keeps on decreasing with the application of the force and it starts breaking at some point. This change in diameter of the rod at neck can be calculated using true and engineering strain.

When an external tensile force is applied to a metal rod. It's diameter keeps on decreasing with the application of force and starts breaking at some point.

Since this change in length and diameter of the test specimen is not sudden. It is decreasing gradually with the application of external force. Engineering and True Strain are different in a way how they measure this change in cross section when external force is applied.

True Strain

True Strain measures the change in length to the original length at various instant of times when external force is applied to the test specimen. In other words, True strain is calculated by measuring the change in length at various time stamps and sum over them along full length.

This image shows the formula to calculate true strain value.
True Strain Calculation Formula
Engineering Strain
This image shows the formula to calculate engineering strain.
Engineering Strain Calculation Formula

Engineering Strain measures the total change in length to the original length when external force is applied to the test specimen. It is a type of linear strain. Engineering Strain or stress is calculated by considering initial length and final length of the test specimen.

To sum up, mechanical strain in a body is used to calculate deformation inside a body when an external force is applied. It is used during product design for failure analysis. We suggest you also read this article on the Stress-Strain curve to understand more about the relationship between engineering stress and strain.

We will keep updating this article on strain in mechanics. You can share your suggestions and questions on strain in mechanical engineering in the comment box.

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