elasticenergy

Elastic energy, or elastic potential energy, is the energy stored in an object when it is deformed by external forces and released when the object returns to its original shape. The concept applies to springs, rubber bands, cables, and many structural members.

For a simple linear spring that obeys Hooke's law, the restoring force is F = -k x and the stored energy is U = 1/2 k x^2, where k is the spring constant and x is the displacement from the rest length. In continuous media, energy can be described by the energy density w = 1/2 σ ε, with σ the stress and ε the strain; the total energy is U = ∫ w dV. For bending beams, energy is related to bending stiffness EI and curvature, often expressed as an integral along the beam.

Elastic energy depends on the magnitude of deformation and material stiffness: larger deformation and stiffer materials store more energy for a given displacement. The unit of energy is the joule (J).

In ideal, perfectly elastic systems, mechanical energy is conserved, exchanging between potential and kinetic forms as objects move. Real materials exhibit damping and hysteresis, dissipating part of the energy as heat, sound, or wear.

Applications include clocks and watches, vehicle suspensions, archery, and energy-storage concepts that use elastic elements to store and release energy efficiently.