<P> Elastic energy of or within a substance isstatic 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 . </P> <P> Although elasticity is most commonly associated with the mechanics of solid bodies or materials, even the early literature on classical thermodynamics defines and uses "elasticity of a fluid" in ways compatible with the broad definition provided in the Introduction above . </P> <P> Solids include complex crystalline materials with sometimes complicated behavior . By contrast, the behavior of compressible fluids, and especially gases, demonstrates the essence of elastic energy with negligible complication . The simple thermodynamic formula: d U = − P d V, (\ displaystyle dU = - P \, dV \,) where dU is an infinitesimal change in recoverable internal energy U, P is the uniform pressure (a force per unit area) applied to the material sample of interest, and dV is the infinitesimal change in volume that corresponds to the change in internal energy . The minus sign appears because dV is negative under compression by a positive applied pressure which also increases the internal energy . Upon reversal, the work that is done by a system is the negative of the change in its internal energy corresponding to the positive dV of an increasing volume . In other words, the system loses stored internal energy when doing work on its surroundings . Pressure is stress and volumetric change corresponds to changing the relative spacing of points within the material . The stress - strain - internal energy relationship of the foregoing formula is repeated in formulations for elastic energy of solid materials with complicated crystalline structure . </P> <P> Components of mechanical systems store elastic potential energy if they are deformed when forces are applied to the system . Energy is transferred to an object by work when an external force displaces or deforms the object . The quantity of energy transferred is the vector dot product of the force and the displacement of the object . As forces are applied to the system they are distributed internally to its component parts . While some of the energy transferred can end up stored as kinetic energy of acquired velocity, the deformation of component objects results in stored elastic energy . </P>

​ stress that is converted to positive energy is called