Stress and strain are important ideas when we try to understand how materials break.

Definitions:

• Stress ($\sigma$) is the amount of force ($F$) put on a material for each area ($A$) of that material. We can write it like this: $\sigma = \frac{F}{A}$ We measure stress in pascals (Pa). To give you an idea, 1 Pa is like a tiny amount of pressure, equal to 1 newton per square meter.

• Strain ($\epsilon$) tells us how much a material changes shape when stress is applied. It isn't measured in specific units but is a fraction: $\epsilon = \frac{\Delta L}{L_0}$ Here, $\Delta L$ is how much the length changes, and $L_0$ is the original length.

Material Response:

• Every material has a limit called the elastic limit. If we push it too far, it may bend permanently or break. For example, steel can handle about 250 megapascals (MPa) before it starts to change shape.

• Young's Modulus ($E$) helps us understand the relationship between stress and strain when a material is still acting normally (the elastic region). We can express it like this: $E = \frac{\sigma}{\epsilon}$ This value shows how stiff a material is. Steel has a stiffness value of about 200 gigapascals (GPa).

Predictive Analysis:

• The ultimate tensile strength (UTS) is the most stress a material can take before it gets stretched too thin, or "necking" occurs. For flexible materials like aluminum, this is about 300 MPa.

• By looking at stress and strain, engineers can figure out safe limits for materials. This way, they can predict when and where something might fail. This is really important to make sure that buildings and structures can hold up without breaking under pressure.