Elastic Energy

Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume or shape. Elasticity theory primarily develops an analytical understanding of the mechanics of solid bodies and materials. The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into another form of energy, such as kinetic. Mathematically, the equation can be stated as

The essence of elasticity is reversibility. Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape. However, all materials have limits to the degree of distortion they can endure without breaking or irreversibly altering their internal structure. Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. Beyond the elastic limit, a material is no longer storing all of the energy from mechanical work performed on it in the form of elastic energy.

Elastic energy of or within a substance is static energy of configuration. It corresponds to energy stored principally by changing the inter-atomic distances between nuclei. Thermal energy is the randomized distribution of kinetic energy within the material, resulting in statistical fluctuations of the material about the equilibrium configuration. There is some interaction, however. For example, for some solid objects, twisting, bending, and other distortions may generate thermal energy, causing the material's temperature to rise. Thermal energy in solids is often carried by internal elastic waves, called phonons. Elastic waves that are large on the scale of an isolated object usually produce macroscopic vibrations sufficiently lacking in randomization that their oscillations are merely the repetitive exchange between (elastic) potential energy within the object and the kinetic energy of motion of the object as a whole.