The stress-strain relationship helps us understand how materials react when we put force on them. Different materials act differently, and here’s how:

1. Elastic Materials: These materials go back to their original shape once the force is taken away. We can describe this with Hooke's Law, which is like a simple rule that says: $\sigma = E \cdot \epsilon$ Here, $\sigma$ means stress (the force put on the material), $E$ is the elasticity (how stretchy the material is), and $\epsilon$ is strain (how much the material stretches).

2. Plastic Materials: These materials change shape and never go back to how they were after a certain point. This point is called the yield point. Once they reach it, they stay deformed.

3. Brittle Materials: These materials break easily when stressed. They don't change shape much before they snap, which can happen suddenly and unexpectedly.

Knowing how these different materials behave helps engineers choose the right ones to keep structures safe and working well!