Strain

Understanding the mechanics of materials is key to engineering applications of these materials. We must understand how these materials deform under various external conditions and various external forces that are applied to them. This involves understanding the internal forces and the associated dimensional changes that the materials undergo.

Particularly important is to understand the properties of the materials used, their strength and their stiffness. This will determine the acceptable limits of their deformation. Thus, understanding these properties is central to the exercise of engineering design. It may seem a mammoth task, but the first step in this journey is to understand the stress-strain relationship (curve). In this article, we start with understanding strain.

Definition of strain

Let’s first understand the definition of strain.

• When an external force is applied to a material, it elongates (changes its length). 

• The ratio of this change in length to the original length is called strain.  

• So when you stretch a rubber band, the difference between the new length and the original length divided by the original length is termed as strain.

Strain is a dimensionless entity and is usually denoted by the symbol ϵ.

Formulaically, the definition of strain is as follows: ϵ = ΔL / L

Where:

• ϵ: Strain

• ΔL: Elongation

• L: The original length

Strain can be positive or negative, depending on whether the external forces applied are tensile or compressive.

Types of strain

There are two basic types of strain that exist: Normal strain and Shear strain.

Normal Strain

When the elongation in a material is caused by normal stress, then it is a normal strain.

Shear Strain

Similarly, when the change in length of the material is due to shear stress, then it is a shear strain.

Hooke’s Law

Hooke’s law simply states that as long as the material is within its elastic limit, the strain is directly proportional to the stress applied.

Stress ∝ Strain

Thus:

σ ∝ ϵ

σ = Y*ϵ

F/A = Y*ΔL / L

Where:

• Y is a constant of proportionality called Young’s modulus or elastic modulus.

• F is applied force

• A is the area on which force is exerted

• ΔL is the change in the length

• L is the original length

• Since strain is dimensionless, Young’s modulus has the same dimensions as stress.

Young’s modulus of elasticity

Simply put, the ratio of stress to strain is called Young’s modulus of elasticity. Where stress is the external force applied per unit area (cross-sectional) and strain is the change in length of the material divided by its original length.

Poisson’s ratio

Say we have a bar to which we have applied longitudinal stress. Depending on the direction of the application of force, a corresponding strain will develop. It has been a common observation for elastic materials that lateral strain is proportional to longitudinal strain.

The ratio of the lateral strain to the longitudinal strain developed is known as Poisson’s ratio. It is usually denoted by the symbol µ.

µ = lateral strain / longitudinal strain

In most of the materials, the value of µ ranges between 0.25 and 0.33.

Conclusion

To summarise the concept of strain, remember that strain is the ratio of the change in length caused by the application of an external force to the original length of the material. There are two basic kinds of strain: Normal strain and shear strain. Strain is a dimensionless quantity and has no unit. Hooke’s law simply states that as long as the material is within its elastic limit, the strain is directly proportional to the stress applied. The ratio of stress to strain is called Young’s modulus of elasticity.