# Deformation

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## 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 ?
The samples were divided into finite elements to model the two dimensional deformations according to the real changes in moisture content of the elements.
However, there are problems with this as a rebuttal of my contention that shock deformation cannot be ruled out in the usual PK metal bending parties that provide most of the evidence for spoon bending.
Deformation in this region is completely recoverable upon removal of the stress.
Localised plastic deformations were researched at deformation states within interval [beta] = (-1/2;0).
Very fine ferrite grains were again found in both microstructures and high hardness values were therefore measured for both strategies, reaching 170 HV10 for strategy with incremental deformation and even 180 HV10 for the strategy with two deformations.
In the mineral wool samples, the precision of measurement of longitudinal deformations by shift of machine's traverse made 0.
to develop a methodology of evaluating the effectiveness of a deformation zone.
A significant factor in terms of the response of the stone structure to non-stress effects is the interaction of the stone bridge structure and the bridge body filler and its interaction with the breast walls, which prominently affects mainly the vertical deformations of the bridge vaults.
Created to help the CFD engineer get the best possible design results in the shortest time, it is an interactive, real-time design deformation software that can arbitrarily alter the shape of a computerized object whose shape is defined by the points of a grid.
Combine the known limitations of MFL and the caliper tool's ability to detect mechanical damage with the evaluation and repair conditions of the regulations and it becomes obvious why there is an apprehension to call a deformation with metal loss and why even plain deformations less than 2% of pipeline diameter go largely unreported.
1) is associated with isotropic deformations, whereas the second term is associated with anisotropic deformations of the arterial wall.

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