# Elasticity [physics]

Elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied to them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.

Elasticity concerns both solid bodies and fluids. Solid bodies have both shape and volume elasticity, that is they react elastically to stresses that tend to deform the volume of the body and to change its angles; fluids, on the other hand, have only volume elasticity, because they react elastically to compression or expansion but do not resist the change in shape, which depends on the container.

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.

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. Elastic energy is potential energy and is stored by changing the inter-atomic distances between nuclei.

## Atomic origin of elastic behavior

The elastic behavior of different materials has microscopic origins that are distinguished by the particular type of material. We can speak in fact of “enthalpy elasticity” and “entropy elasticity”.

### Crystalline materials

Enthalpic elasticity is characteristic of crystalline materials, and derives from a phenomenon that occurs at the atomic level. The elastic properties of these materials derive from the type of interaction that takes place between their constituent atoms, when they are subjected to an external load. If these interactions determine a displacement of the atoms contained, these, once the load is removed, are able to reoccupy their initial position and the material is called elastic; if moreover the displacement is sufficiently small, the direct proportionality between deformation and load is guaranteed and therefore Hooke’s law is valid.

The dense crystalline lattice of these materials allows only small deformations and local displacements, hence the high elastic limit and the large elastic modulus. This results in the necessity to exert high stresses to obtain relevant deformations. In the case of remaining below the yield stress of the material, the relationship between stress and strain is equal to the constant elastic modulus or Young’s modulus, which represents the proportionality between stress and strain in the linear range of the material, described by Hooke’s law.

Elasticity therefore depends on the microscopic structure of the material and on the interaction forces acting between the atoms composing it. In particular, the potential energy existing between each pair of atoms must be considered, which can be expressed as a function of their distance. At a certain distance the two atoms are in equilibrium, i.e. the resultant of interaction forces between them is zero. The variation of these forces (due to external stress) makes the mutual distance between the particles vary (producing at macroscopic level the deformation of the body: in the case of traction, for example, there is a “stretching” of the bonds).

For relatively low levels of stress, the mechanical work required is accumulated as elastic energy, inside the material, and is returned in full at the absence of the soliciting cause while the particles return to their initial position (the body regains its original shape and size).

### Non-crystalline materials

Entropic elasticity is characteristic of polymeric materials made up of chains at the molecular level; this elasticity results from a movement of the chains from a high entropy state (the most likely state, where the chains are entangled) to a low entropy state (a less likely, more ordered state, where the chains are aligned), which occurs during elongation of the material.

Polymeric materials such as rubber, being composed at the microscopic level of chain molecules, allow for large sliding and deformation, and therefore are characterized by low elasticity limits and small modulus of elasticity. This means that relatively low stresses and strains already correspond to macroscopically appreciable deformations, as well as very low yield or rupture points. These materials are called elastomers, with a so-called “high elasticity” behavior compared to the “true elasticity” of crystalline materials. In addition, due to early stretching of the chains, caused by further elongation when they have already been aligned, elastomers have nonlinear elastic behavior.

### Cellular materials

Cellular materials, such as wood, react differently to compression and tension. Due to the presence of cavities in the material, compression shows complete stiffness until the walls of these cavities are subjected to elastic deflection, which allows for significant deformation without much increase in stress. Moreover, these deformations are largely recoverable, but once they occur they bring the body back to a state of rigidity, the cavities having been cancelled. On the other hand, these do not have the same influence on traction, which does not allow elastic bending of the walls in the same way.

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