8.5.4. POISSON'S RATIO

The strain perpendicular to the applied force is called lateral strain. Simon Poisson pointed out that within the elastic limit, lateral strain is directly proportional to the longitudinal strain.

In any material being stretched or compressed, there is a change not only in its length (which we call longitudinal strain) but also in its width or diameter. The lateral strain refers specifically to this change in dimensions that occurs perpendicular to the direction of the applied force. Simon Poisson observed that under elastic conditions, the amount a material contracts or expands laterally is proportional to how much it stretches or compresses longitudinally. This relationship helps engineers and scientists understand how materials behave under stress.

Think about a balloon. When you blow up a balloon (applying longitudinal stress), it not only expands in length but also gets wider (lateral strain). If the balloon is stretched too much, it will pop; similarly, materials under stress can only undergo this kind of stretching and compressing up to a certain point—the elastic limit—before they deform permanently.

The ratio of the lateral strain to the longitudinal strain in a stretched wire is called Poisson’s ratio. If the original diameter of the wire is d and the contraction of the diameter under stress is ∆d, the lateral strain is ∆d/d. If the original length of the wire is L and the elongation under stress is ∆L, the longitudinal strain is ∆L/L. Poisson’s ratio is then (∆d/d)/(∆L/L) or (∆d/∆L) × (L/d). Poisson’s ratio is a ratio of two strains; it is a pure number and has no dimensions or units.

Poisson's ratio is mathematically defined as the ratio of lateral strain (how much the diameter decreases) to longitudinal strain (how much the wire stretches). The formula shows how both strains depend on their respective initial dimensions. This means if you know how much a wire is stretched, you can calculate how much it will also become thinner. Importantly, Poisson's ratio is dimensionless, meaning it does not have physical units—it simply describes the proportional effect of one strain on another.

Imagine squeezing a sponge. As you squeeze it from the sides (longitudinal strain), it becomes thinner (lateral strain). The extent to which it becomes thinner compared to how much you are squeezing it is analogous to Poisson's ratio. Just like the sponge, different materials will react differently when forces are applied, showing various Poisson's ratios.

Its value depends only on the nature of material. For steels, the value is between 0.28 and 0.30, and for aluminium alloys, it is about 0.33.

Different materials have unique properties that determine their behavior under stress, which includes their Poisson's ratio. For instance, steel, which is known for its strength and durability, typically has a Poisson's ratio value around 0.28 to 0.30, meaning it will contract in width moderately when stretched. Aluminium alloys, which are lighter and more malleable compared to steel, have a value slightly higher at about 0.33. These values give engineers and designers critical information on how materials will perform in real applications.

Think of steel and aluminium in a construction context. If you're building a bridge, knowing that steel has a lower Poisson's ratio means it will maintain its shape better under load, whereas aluminium might experience more significant changes in dimensions under the same conditions. Thus, understanding these properties helps in selecting the right materials for different engineering projects.

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