Hooke's Law

In 1676, the English physicist Robert Hooke, studying how much a wire stretches under tension, discovered a simple relationship between stress and strain that now bears his name. Hooke's law states that, within the elastic limit, stress is directly proportional to strain:

This constant of proportionality is called the modulus of elasticity of the material. Equivalently, the modulus of elasticity is defined as the ratio of stress to the corresponding strain, and geometrically it is the slope of the straight-line portion of the stress-strain graph (Fig. 6.4) — the portion in which the material's elastic deformation is proportional to the applied stress. Because different materials resist deformation differently, the value of this modulus depends entirely on the nature of the material (a stiff material like steel has a much larger modulus than a soft one like rubber).

The maximum stress up to which stress remains directly proportional to strain — that is, up to which Hooke's law continues to hold — is called the elastic limit of the material. Beyond this point, as later sections (6.6, the stress-strain curve) describe in detail, the simple proportionality between stress and strain breaks down even though the material may still recover fully when unloaded, right up to a somewhat higher stress called the yield point. …