Elasticity (physics)

Basic concepts

Two central quantities in elasticity are stress and strain. Stress is the internal force per unit area that develops in a body when external forces act on it; strain measures the relative change in shape or length. For small deformations many materials follow a linear relation often called Hooke's law, which states that stress is proportional to strain. The proportionality constant in simple tension is known as Young's modulus, one example of an elastic modulus.

Common elastic parameters

• Young's modulus — stiffness in uniaxial tension or compression.
• Shear modulus — resistance to shape change at constant volume.
• Bulk modulus — resistance to uniform compression.
• Poisson's ratio — transverse contraction relative to axial extension.

More generally, elasticity in three dimensions is described by stress and strain tensors and, for linear materials, by a stiffness (or compliance) tensor that links them. Isotropic materials require only two independent elastic constants; anisotropic crystals can require many more.

History and development

The idea that elastic forces restore a body toward equilibrium was put in mathematical form in the 17th century by Robert Hooke, who studied springs and stated the proportional relation now called Hooke's law. Later work expanded the theory into continuum mechanics, introducing tensor descriptions, energy methods, and generalized constitutive laws for nonlinear or large-strain elasticity.

Applications and distinctions

Elasticity governs the behaviour of everyday objects such as springs and a rubber band, and it is crucial in engineering design, seismic wave analysis, materials science, and biomechanics. Important distinctions include:

1. Elastic vs plastic: elastic deformation is reversible; plastic is permanent beyond the yield point.
2. Linear vs nonlinear: linear elasticity holds for small strains; many materials show nonlinear or hyperelastic responses at large strains.
3. Elastic vs viscoelastic: viscoelastic materials show time-dependent recovery and energy dissipation.

Ideal elastic materials store mechanical energy during deformation and release it when unloaded; real materials may show hysteresis and energy loss. Understanding elastic behaviour enables prediction of stresses, deflections, and wave speeds in solids, making it a foundational topic in physics and engineering.