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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 ?
In these composites, the contribution of fiber fragmentation events to the onset of inelastic deformations at [[Epsilon].
This expression was used in combination with typical equations of plasticity, regarding inelastic deformations.
It is shown that 1) the volumetric expansion due to inelastic deformation occurs depending on the material even if the current value of the first stress invariant is negative, 2) an overstress theory proposed by Krempl fairly well describes the stress-strain curves of both POM and PMMA at the strain paths without strain reversal, and 3) in the stress relaxation or the creep executed after strain reversal, an unexpected behavior in which the stress rate or the strain rate may change its sign depending on the test condition is observed.
For each principal stress, a trial damage deformation rate, [Mathematical Expression Omitted], is first computed by assuming that the increment in inelastic deformation is entirely due to damage.
During a typical accident, the foam is expected to absorb a significant amount of energy by undergoing large inelastic deformations.
Such an approach seems to ignore the fundamental differences of the mechanisms of inelastic deformation in metals and polymers.
o] is the limiting strength, and p and q are material dependent parameters, which are, in theory, determined by the mechanism of inelastic deformation.
This can result in a building design that does not fully take advantage of its ability to accommodate inelastic deformations, which can, in return, result in extra construction costs.
Another form of answer is by means of inelastic deformations, once deformed the object, this is not able to recover the original form.
Splits, cracks, hollow parts, foreign inclusions and displacements within the particle have the effect of increasing internal source of inelastic deformations and fractures.
Some noncrosslinked polymers are capable of sustaining very large inelastic deformations before eventual failure.