Spring elasticity and spring potential energy

The potential energy generated by the elastic deformation of an object and the interaction of the elastic forces between various parts is called "elastic potential energy", which is also called "elastic deformation energy" in engineering. For example, a compressed gas, a curved bow, a winding spring, a stretched or compressed spring all have elastic potential energy.

Elastic potential energy is the potential mechanical energy stored in the construction of a material or physical system because work is done to deform its volume or shape when compression and stretching are required, or when deformation occurs in essentially any way. The theory of elasticity was developed primarily in the form of solid and material mechanics [1](note that the work done by stretching a rubber band is not an example of elastic potential energy, it is an example of entropic elasticity), and the elastic potential energy equation is used to calculate the mechanical equilibrium position. Mathematically, this equation can be stated as [2]:

The unit of potential energy is the same as the unit of work in order to determine the size of the elastic potential energy, we should choose the zero potential energy state. In general, the spring is chosen without any deformation, but in the free state its elastic potential energy is zero. The work done by the elastic force on the body is equal to the negative of the increase in elastic potential energy. In other words, the work done by the elastic force is only related to the extension of the spring in the initial and final state, and has nothing to do with the deformation process of the spring. Elastic potential energy presupposes the existence of an elastic force, so elastic potential energy is possessed by a body that has elastic deformation and elasticity between its parts. If the interaction between two bodies deforms, then each body has an elastic potential energy, and the total elastic potential energy is the sum of the two

Elasticity is essentially reversible in that the force applied to an elastic material transfers energy into the material and can restore its original shape after the energy is transferred to its surroundings. However, all materials have a limit to how much deformation they can withstand without destroying or irreversibly changing their internal structure. Therefore, the properties of solid materials usually include the specification of the elastic limit of strain. Beyond the elastic limit, the material no longer stores in the form of elastic energy all the energy of mechanical manipulation on it.

The elastic energy within or within a substance is the static energy of the configuration which corresponds to the energy stored primarily by changing the atomic spacing between the nuclei. Thermal energy is the random distribution of kinetic energy in the material, resulting in statistical fluctuations in the material near the equilibrium configuration. But there are some interactions - for example, for some solid objects, twisting, bending, and other deformations can generate thermal energy, causing the material to heat up. Heat energy in solids is usually achieved by internal elastic waves called phonons. Large-scale elastic waves of isolated objects usually produce macroscopic vibrations that lack sufficient randomness, and their vibrations are just repeated exchanges between the (elastic) potential energy in the object and the kinetic energy of the whole object's motion.

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