# Deformation

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Related to permanent deformation: Plastic deformation

## deformation

[‚def·ər′mā·shən]
(mathematics)
A homotopy of the identity map to some other map.
(mechanics)
Any alteration of shape or dimensions of a body caused by stresses, thermal expansion or contraction, chemical or metallurgical transformations, or shrinkage and expansions due to moisture change.

## Deformation

An act of deforming or changing the shape or an alteration in form that a structure undergoes when subjected to the action of a weight or load.

## Deformation

the change in the relative positions of the particles of a body associated with their displacement. It results from a change in interatomic distances and the regrouping of blocks of atoms. Deformation is usually accompanied by an alteration in the magnitudes of the interatomic forces, a measure of which is elastic stress.

The simplest forms of deformation of a body as a whole are extension-compression, shear, flexure, and torsion. In most cases the observed deformation is a number of types of deformation simultaneously. Ultimately, however, it is possible to reduce any deformation to two of the simplest forms, extension (or compression) and shear. The deformation of a body is completely determinable if the displacement vector for each of its points is known. The deformation of solids in connection with their structural peculiarities is studied in solid-state physics, and the displacements and stresses in solids that are being deformed are investigated by the theory of elasticity and plasticity. In liquids and gases, whose particles have high mobility, the study of deformation is replaced by the study of instantaneous velocity distribution.

Deformation of a solid can be manifested as a consequence of phase transitions associated with a change in volume and with thermal expansion, magnetization (the magnetostrictive effect), and the appearance of an electric charge (the piezoelectric effect), or as a result of the action of external forces. The deformation is called elastic if it disappears after the removal of the load that caused it and plastic if it does not disappear (or does not disappear completely) after the load is removed. Upon deformation all real solids have plastic properties to a greater or lesser extent. Under certain conditions the plastic properties of bodies may be disregarded, as is done in elasticity theory. A solid may with sufficient accuracy be considered elastic, that is, not exhibiting appreciable plastic deformation, as long as the load does not exceed a certain limit.

The nature of plastic deformation may vary depending on temperature, the duration of action of the load, and the rate of deformation. If the load applied to the body is constant, the deformation changes with time; this phenomenon is called creep. The creep rate increases with temperature. Relaxation and elastic aftereffect are special cases of creep. Relaxation is the process of spontaneous decrease in internal stress over time at constant deformation. The process of spontaneous increase in deformation at constant stress is called an aftereffect. One of the theories explaining the mechanism of plastic deformation is the theory of dislocations in crystals.

In the theory of elasticity and plasticity, bodies are regarded as continuous. Continuity, which is the ability to fill the entire volume occupied by the material of a body, without any empty space, is one of the basic properties ascribed to real bodies. The concept of continuity also applies to the elementary volumes into which a body can be divided mentally. A change in the distance between the centers of each of two contiguous infinitely small volumes in a body not subject to fracture must be small compared with the initial value of that distance.

The simplest elementary deformation is the relative elongation of a certain element: є = (l1- 1)ll, where l1 is the length of an element after deformation and l is the original length of the element. In practice, small deformations are more often encountered, so that є < < 1.

Deformation is measured either in the process of testing materials to ascertain their mechanical properties or in the study of structures by actual measurement on them or on models to evaluate the stresses. Elastic deformations are quite small, and high accuracy is necessary when measuring them. Strain gauges are most generally used to study deformation. Extensive use is also made of resistance strain gauges, the optical polarization method of studying stresses, and X-ray structural analysis. In assessing local plastic deformation, a grid is etched on the surface of an article or the surface is covered with an easily cracked lacquer.

### REFERENCES

Rabotnov, Iu. N. Soprotivlenie materialov. Moscow, 1950.
Kuznetsov, V. D. Fizika tverdogo tela, vols. 2-4, 2nd ed. Tomsk 1941-47.
Sedov, L. I. Vvedenie v mekhaniku sploshnoi sredy. Moscow, 1962.

## deformation

Any change of form, shape, or dimensions produced in a body by a stress or force, without a breach of the continuity of its parts.
References in periodicals archive ?
This test simulates the passage of moving traffic loads on the pavement to study the permanent deformation characteristics of bituminous materials and its ability to resist the creep distress under repeated load.
The parameters [G.sup.*.sub.g] and [f.sub.c] depict the resistance to permanent deformation in asphalt mixtures at low temperatures.
In general, the higher the stiffness, the better its resistance to permanent deformation and it improved the resistance to rutting [10].
The rheological characterization of the recovered binder (ASTM D1856) suggests that this binder should provide good resistance to permanent deformation. Both the complex modulus and the storage modulus are very high at 60 [degrees] C The results support the notion that the binder in the loose mix is superior to the RTFO aged residue.
Generally, most of the experimental results show that permanent deformation buildup of coarse grained soils under repeated loading is actually a ceaseless gradual process, which means that in each load repetition a small strain increment will be accumulated to the total deformation.
To this end, most of the relevant studies have focused on the effects of CAA on the resistance to permanent deformation and skid resistance of HMA.
Hence, more energy dissipates by the permanent deformation rather than transmission when less than half of the surface is in contact.
Permanent deformation for the upper sheet reached conformity level at 77%.
The MCC was also found to increase the elastic recovery of strain in recovery process and reduce the permanent deformation which is an important factor in dimensional stability of polymer materials when the load is removed.
The lower the percentage, the better the material resists permanent deformation under a given deflection and temperature range.
In addition, it is interesting to understand not only how permanent deformation is solved across the lithosphere but which regions are actually under reversible and permanent deformation.

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