Hooke's law

In the field of linear elasticity, Hooke's law relates the deformation to the exerted stress using the Young modulus.

In 1678, Robert Hooke (1635-1703), an English astronomer and mathematician born in Freshwater, established through experiments that in linear elasticity, the extension of a structure in a given direction was proportional to the applied load in that direction, and this held for several materials.

In the case of tensile stress and unit extension per unit volume, Hooke's law takes the form (1).

When generalised in matrix form, Hooke's law relates the components defining the deformation state at a point to the components of the stress state at the same point (formula (2)).

Hooke's law is fundamental to the strength of materials and continuum mechanics.