law of elasticity discovered by the English scientist Robert Hooke (Hooke, Robert) in 1660, which states that, for relatively small deformations (deformation and flow) of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load. Elastic behaviour of solids according to Hooke's law can be explained by the fact that small displacements of their constituent molecules, atoms, or ions from normal positions is also proportional to the force that causes the displacement.

The deforming force may be applied to a solid by stretching, compressing, squeezing, bending, or twisting. Thus a metal wire exhibits elastic behaviour according to Hooke's law because the small increase in its length when stretched by an applied force doubles each time the force is doubled. Mathematically, Hooke's law states that the applied force F equals a constant k times the displacement or change in length x, or F=kx. The value of k depends not only on the kind of elastic material under consideration but also on its dimensions and shape.

At relatively large values of applied force, the deformation of the elastic material is often larger than expected on the basis of Hooke's law, even though the material remains elastic and returns to its original shape and size after removal of the force. Hooke's law describes the elastic properties of materials only in the range in which the force and displacement are proportional. (See deformation and flow.) Sometimes Hooke's law is formulated as F=−kx. In this expression F no longer means the applied force but rather the equal and oppositely directed restoring force that causes elastic materials to return to their original dimensions.

Hooke's law may also be expressed in terms of stress and strain. Stress is the force on unit areas within a material that develops as a result of the externally applied force. Strain is the relative deformation produced by stress. For relatively small stresses, stress is proportional to strain. For particular expressions of Hooke's law in this form, see bulk modulus; shear modulus; Young's modulus.