# Hooke's Law - Stress And Strain

Hooke’s law was studied by the 19th-century English scientist Robert Hooke in which he noticed that many materials exhibited a property when the stress-strain relationship was studied. There was a linear region where the force required to stretch the material such that it was proportional to the extension of the material.

## What is Hooke’s Law?

Hooke’s law states that

the strain of the material is proportional to the applied stress within the elastic limit of that material.

Hooke’s law is also known as Hooke’s law of elasticity as the elastic materials obey Hooke’s law. When the elastic materials are stretched, the atoms and molecules deform until stress is been applied and when the stress is removed they return to their initial state.

## Hooke’s Law Formula

Hooke’s law formula is given as:

 F = -k.x

Where,

• F is the force
• x is the extension length
• k is the constant of proportionality known as spring constant in N/m

### Hooke’s Law Experiment

Consider a spring with load application as shown in the figure.

Different springs, depending on the material, will have different spring constants. This can be calculated. The constant calculated empirically can be used further. The figure shows us three instances, the stable condition of the spring, the spring elongated to an amount x under a load of 1N, and the spring elongated to 2x under a load of 2N. If we plug in these values into the equation above we get the spring constant for the material in consideration.

 σ = Eε

Where,

• σ is the stress
• E is the modulus of elasticity also known as Young’s modulus
• ε is the strain

When the stress is removed from the material, there are two types of deformation that can take place: plastic deformation and elastic deformation

### Hooke’s Law Graph

The figure below shows the stress-strain curve for low carbon steel.

From the origin till the proportional limit nearing yield strength, the straight line implies that the material follows Hooke’s law. Beyond the elastic limit between proportional limit and yield strength, the material loses its elastic nature and starts exhibiting plasticity. The area under the curve from origin to the proportional limit falls under the elastic range. The area under the curve from a proportional limit to the rupture/fracture point falls under the plastic range.

The ultimate strength of a material is defined based on the maximum ordinate value given by the stress-strain curve (from origin to rupture). The rupture strength is given by the value at a point of rupture.

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