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A homotopy of the identity map to some other map.
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.


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.



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.


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.


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 ?
With the newly-developed hot deformed neodymium magnet, Daido Steel will make a new entry into the market for magnets used for drive motors of hybrid vehicles, which has been basically monopolized by sintered neodymium magnets.
Thalidomide babies often suffered missing or deformed limbs and extreme shortening of arms and legs, but the drug also caused malformations of the eyes and ears, genitals, heart, kidneys and digestive tract.
For 0 < d < 1, minima are present both at non-zero [beta] and at [beta] = 0, with the deformed minimum lower 0 < d < 8/9 and the undeformed minimum lower for 8/9 < d < 1.
When asked if he could seriously compare a disabled child to a deformed lamb, independent Mr Brewer said: "The cost has to be evaluated.
The lead detected in the Gulf of Finland was surrounded by thick deformed ice (up to 5 m) between Helsinki and Tallinn.
However, we do not yet know why these particular skulls were deformed.
They found that smoking while pregnant increased the risk of having a baby with missing or deformed limbs by 26%.
Feng Hsin now quotes scrap steel at NT$12,900 per metric ton and deformed bar at NT$20,600, and NT$21,800 per metric ton for steel H-beam.
Titanium crystals of a certain size are deformed in a way that each atom is systematically displaced in proportion to the neighbouring atoms, which results in a macroscopic deformation.
The absorbent article is deformed such that a concavity is formed on the topsheet side, the absorbent article being put on a wearer while maintaining such a deformed configuration by the sheet-like member.
In the initial stage, these spots appear in the form of separate dark areas which in further stages, especially at the start of fracture, may extend to the entire grain and occupy a large part of the deformed section.
At sites 2 and 3, the percentages of deformed fruit and normal fruit were estimated by randomly selecting 5 trees in each orchard and classifying every off bloom fruit on the tree as either being "normal" or "deformed.