Hooke's Law

8.3 Hooke’s Law

When a solid is deformed by an external force, the atoms or molecules are displaced from their equilibrium positions. For small deformations, the restoring force that develops inside the material is directly proportional to the deformation itself. This linear relationship between stress and strain is the essence of Hooke’s law.

The constant of proportionality $k$ is called the modulus of elasticity of the material. Its value depends on the material and on the type of deformation (tensile, compressive, or shear). Because strain is dimensionless, the modulus of elasticity has the same unit as stress — pascal (Pa) or N m$^{-2}$.

Hooke’s law is an empirical law — it was discovered through experiment, not derived from first principles. It holds for most solid materials when the deformation is small. However, some materials do not obey this linear relationship even at very small strains; rubber and biological tissues are examples. …