Dimensions of Strain

It is the response of any system to the stress applied to it. When a material is given some force, it tends to produce stress which then causes the material to deform. Strain is an important concept of physics, in this concept, the number shows the relative deformation or change in shape and size of elastic, plastic, and fluid materials under applied forces. Strain causes deformation that arises through the material as the particles in it are slightly displaced from their normal position. The amount of deformation in the direction of applied force divided by the earlier length of the material is called engineering strain. It results in a unitless number which is often also left in non-simplified form like inches per inch or meters per meter.

In the case of stress, the distribution of strain may or may not be uniform in a complex structural element, also depending on the nature of the loading condition.

Let’s understand with an example where the strain in a bar that is being stretched in tension is the amount of elongation or change in length that is divided by its original length. On the other hand, if we talk about stress here, the strain may/may not be uniform in a complex structural element depending on the nature of the loading condition.

Strain= Elongation / Original Length

It can be represented by, Strain = ∆L/L⁰

Further, we can know that if the stress is small on the material, it may only strain by a small amount and return to its original size after the release of stress. It is called elastic deformation because similar to elastic, it returns to its unstressed state. Elastic deformation is known to occur in a material when stresses are lower than critical stress (also known as yield strength). If the material is stressed further to its elastic limit, the material remains in a deformed condition after the removal of the load and this is called plastic deformation.

True strain measures account for changes in cross-sectional area by using the instantaneous values of the area.

Strains are further divided into two types: Normal strain and shear strain, and the division is on the basis of the forces that form the deformation. A Normal strain is a type of strain that is caused by forces perpendicular to the plane or cross-sectional area of the material, like that in a rod that is pulled or compressed lengthwise or in a volume that is under pressure on all sides. On the other hand, a shear strain is a type of strain that is caused by forces that are parallel to, and lie in, planes or cross-sectional areas, for example in a short metal tube that is twisted about its longitudinal axis.

Dimensional Formula of Strain

The dimensional formula of Strain is represented as:

\[(M^{0}L^{0}T^{0})\]

Where,

• M = Mass

• L = Length

• T = Time

Derivation

\[Strain = Change in dimension \times Original dimension^{-1}....(i)\]

The dimensional formula of length = \[(M^{0}L^{1}T^{0})....(ii)\]

On substituting equation (ii) in equation (i) we get,

Strain \[= M^{0}L^{1}T^{0} \times (M^{0}L^{1}T^{0})^{-1} = (M^{0}L^{0}T^{0})\]

Therefore, the dimensional formula of strain is represented as \[(M^{0}L^{0}T^{0})\], which is a Dimensionless Quantity.

Types of Strain

There are basically four types of strain defined : 

• Longitudinal Strain: Longitudinal Strain is the type of strain that is described when the deforming force produces a change in the initial length of the given body in the direction of force, then the strain that is produced in the body is called Longitudinal strain. Longitudinal Strain is equal to the ratio of change in length of a body to its original length.

Longitudinal strain : ε = δ / L

• Longitudinal strain is further divided into two types : 

1. Compressive Strain: Compressive Strain is the strain that occurs when the deforming force increases the area of the body and decreases the length of the body, the strain produced is called compressive strain.

2. Tensile Strain: Tensile Strain is the strain that occurs when the deforming force decreases the area of the body and increases the length of the body, the strain produced is called tensile strain.

• Lateral Strain: It is the type of strain that is defined when the deforming force forms a change in length of the given body perpendicular to the direction of force, then the strain produced in the body is called Lateral strain.

• Volumetric Strain: It is the type of strain that is defined when the deforming force produces a change in volume of the given body, then the strain that is formed in the body is called Volumetric strain. Volumetric Strain is equal to the ratio of change in volume of a body to its original volume.

Volumetric Strain = dV / V

• Shearing Strain: It is the type of strain that is defined when the deforming force forms a change in the shape of a body without any change in the volume, then the strain produced in the body is known as the Shearing strain. Shearing strain is basically the angular displacement of the plane perpendicular to the fixed surface. 

Shear Strain = θ = ΔL / L