Young’s modulus is a fundamental property that quantifies a material’s stiffness by establishing the relationship between stress and strain.

Also referred to as the modulus of elasticity, Young’s modulus measures how a material responds to external forces. It is defined as the ratio of stress to strain when a material is subjected to tension or compression. Here, stress is the force applied per unit area, denoted as $\sigma$, while strain is the relative deformation or change in shape of the material, represented as $\varepsilon$.

The mathematical relationship between Young’s modulus, stress, and strain is given by the equation:

In this equation, $E$ represents Young’s modulus. This relationship illustrates that as stress increases, strain also increases, albeit at a diminishing rate. Consequently, a material exhibits greater stiffness as stress levels rise.

Young’s modulus plays a crucial role in material science and engineering, as it indicates how much a material will deform under a specified load. Materials with a high Young’s modulus are characterized by increased stiffness and reduced likelihood of deformation, whereas those with a low Young’s modulus are more flexible and prone to significant deformation.

In engineering applications, Young’s modulus is essential for designing structures and assessing material strength. It is also used to compare the properties of various materials, aiding in the selection of the most suitable material for specific applications.