Stress and strain are fundamental concepts in physics that characterize how materials respond to external forces.

Stress is defined as the force exerted on a material per unit area, and it is typically measured in pascals (Pa), which corresponds to newtons per square meter ($\text{N/m}^2$). In contrast, strain refers to the deformation or change in shape that occurs in the material as a result of this applied stress. Unlike stress, strain is a dimensionless quantity, representing the relative change in size or shape of the material.

When an external force is applied to a material, it generates stress, leading to a deformation that is termed strain. The extent of this deformation is influenced by the material’s inherent properties, such as its elasticity and tensile strength. Strain can be quantitatively expressed as a percentage of the material’s original dimensions.

The relationship between stress and strain is governed by a material’s modulus of elasticity, a measure that indicates how much stress is needed to achieve a specific amount of strain. This relationship is encapsulated in Hooke’s Law, which states that, within the elastic limit of the material, stress is directly proportional to strain for small deformations. The mathematical expression of Hooke’s Law can be represented as:

where $\sigma$ is the stress, $E$ is the modulus of elasticity, and $\epsilon$ is the strain. However, for larger deformations, this linear relationship may no longer hold, and the interaction between stress and strain can become more complex, influenced by factors such as the material’s composition, temperature, and loading conditions.

In conclusion, stress and strain are crucial concepts that describe the mechanical behavior of materials under external forces. Stress is the force applied per unit area, while strain is the resulting deformation or change in shape. The relationship between stress and strain is articulated through a material’s modulus of elasticity and can vary based on different material properties and circumstances.