Hooke's Law

For small deformations, the stress in a solid is DIRECTLY proportional to the strain: stress = E × strain. This is Hooke's law.

The proportionality constant E is the MODULUS OF ELASTICITY — material-specific, geometry-independent.

Stress = force per unit area (N/m² = Pa). Strain = fractional deformation (dimensionless).

Three types of stress/strain: tensile/compressive (longitudinal), volumetric (bulk), shear (tangential).

Each has its own modulus: Young's (Y) for longitudinal, Bulk (B) for volume, Shear (G) for shape.

Linear region: Hooke's law holds. Beyond the proportional limit, the curve deviates.

Spring force F = −kx is a special case of Hooke's law applied to a spring; k = stiffness.

Elastic deformations are REVERSIBLE — strain disappears when stress is removed. Beyond the elastic limit, deformation is permanent (plastic).