Stress and Strain — Definition

Definition

Imagine you have a rubber band. When you pull it, you're applying an external force. This force tries to change the rubber band's shape or size. Inside the rubber band, its constituent particles resist this change, generating internal forces that try to bring it back to its original shape. This internal resisting force, distributed over the cross-sectional area of the rubber band, is what we call stress. Think of it as the 'intensity' of the internal battle against deformation.

More formally, stress ($sigma$) is defined as the internal restoring force ($F$) acting per unit cross-sectional area ($A$) of the body. So, $sigma = F/A$. Its SI unit is Newton per square meter ($N/m^2$), which is also known as Pascal ($Pa$). Stress is a tensor quantity, but for NEET purposes, we often treat it as a scalar or vector depending on the context of normal or shear stress.

Now, what happens when you pull the rubber band? It stretches! The amount by which it stretches, relative to its original length, is called strain. Strain ($epsilon$) is a measure of the deformation itself.

It's the ratio of the change in dimension (like change in length, volume, or angle) to the original dimension. For instance, if a wire of original length $L$ stretches by $Delta L$, the longitudinal strain is $Delta L / L$.

Since strain is a ratio of two similar quantities, it is a dimensionless quantity and has no units.

So, in simple terms: Stress is the cause (internal resistance to deformation), and Strain is the effect (the actual deformation). When an external force acts on a body, it causes deformation. This deformation, in turn, generates internal restoring forces within the material.

These internal forces, per unit area, are stress, and the fractional deformation is strain. Understanding these two concepts is crucial for studying how materials behave under various loads, from simple stretching to complex twisting or compression.