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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


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.
Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



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.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


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.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.
References in periodicals archive ?
This result agrees well with experimental observations [9] that the DE more often suffers the pull-in instability at low stretch rates when inelastic deformation is significant.
Firstly, the damage evolves linearly to D [equivalent to] 0.4 during the second stage (i.e., 10%[N.sub.f]~80%[N.sub.f]), when the coupling of stiffness degradation and inelastic deformation is taken into account.
Change in x-Displacement under Relaxation Process of Elastic and Inelastic Deformation. To display the relaxation process of elastic and inelastic deformation, we used the degree of x-displacement of each atom as the structural indicator, as shown in Figure 2.
The experiment was repeated on the cracked specimens (vertical [II] and horizontal [III]), which were preprocessed to eliminate the effects of inelastic deformation as a consequence of incomplete crack closure.
Based on the parametric study, it is suggested that [l.sub.e]/[l.sub.d,AASHTO] should be larger than 1.5 to develop the full strength of the CISS pile-to-RC pier connection and a considerable inelastic deformation in reinforcing bar simultaneously.
Three characteristic features of the model are to be mentioned: (i) strain energy density is presented as the sum of mechanical energies stored in individual chains and the energy of their interaction with crystallites, (ii) the plastic strain tensor is split into the sum of two components that reflect inelastic deformations in the crystalline and amorphous phases, and (iii) damage accumulation under cyclic deformation is thought of as a two-step process that involves lamellar fragmentation and alignment of broken lamellar pieces along the direction of loading.
The sequence of member yielding, inelastic deformation of critical members, maximum interstorey drifts and the possible collapse mechanisms of the buildings can be determined based on pushover analysis results.
For this group, a 50 percent increase in load produced a 360 percent increase in permanent deflection, because joints subjected to the ultimate impact experienced large inelastic deformations while the load was at the spike maximum.
According to inherent characteristic of PTED connections, it is expected that the proposed connection minimizes inelastic deformation in comparison with the T-Stub moment connections without posttensioning.
In fact, adequate material and structural design is necessary for polymeric systems to exhibit SM behavior, that is, to restore the temporarily fixed residual inelastic deformation once reheated to the rubbery state.
The typical internal variable model, proposed by Chang and Aifantis [9], has described in detail a constitutive framework to consider inelastic deformation based on the notion of internal strain and internal spin tensors together with their precise micromechanical origin.