-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.

In 1934, Polanyi, at about the same time as G. I. Taylor and Egon Orowan, realised that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations which had been developed by Vito Volterra in 1905.

The classical theory of elasticity deals with the behaviour of elastic solids under small deformations, for which ,( 1 ) according to Hooke's Law, stress is directly proportional to the strain — but independent of the rate of strain, or how fast the deformation was applied, and ( 2 ) the strains are completely recoverable once the stress is removed.

Mechanical deformation of hard tissues ( like wood, shell and bone ) may be analysed with the theory of linear elasticity.

As explained before, this theory is not a violation of Poincaré symmetry as much as a deformation of it and there is an exact de Sitter symmetry.

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body.

An idealized uniaxial stress-strain curve showing elastic and plastic deformation regimes for the deformation theory of plasticity

One is deformation theory ( see e. g. Hooke's law ) where the stress tensor ( of order d in d dimensions ) is a function of the strain tensor.

In 1934, Egon Orowan, Michael Polanyi and Geoffrey Ingram Taylor, roughly simultaneously, realized that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations.

The more correct mathematical theory of plasticity, flow plasticity theory, uses a set of non-linear, non-integrable equations to describe the set of changes on strain and stress with respect to a previous state and a small increase of deformation.

Although both FitzGerald and Lorentz alluded to the fact that electrostatic fields in motion were deformed (" Heaviside-Ellipsoid " after Oliver Heaviside, who derived this deformation from electromagnetic theory in 1888 ), it was considered an Ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones.

For example, in Riemann surface theory, the deformation theory of complex structures is studied classically by means of quadratic differentials ( namely sections of L ( K < sup > 2 </ sup >)).

The deformation theory of complex structures and complex manifolds was described in general terms by Kunihiko Kodaira and D. C. Spencer.

The category of group schemes is somewhat better behaved than that of group varieties, since all homomorphisms have kernels, and there is a well-behaved deformation theory.

In 1934, Taylor, roughly contemporarily with Michael Polanyi and Egon Orowan, realised that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations developed by Vito Volterra in 1905.

In a second research phase, Kodaira wrote a long series of papers in collaboration with D. C. Spencer, founding the deformation theory of complex structures on manifolds.

The deformation theory of such submanifolds was studied by McLean.

The mathematical treatment of type IIB string theory belongs to algebraic geometry, specifically the deformation theory of complex structures originally studied by Kunihiko Kodaira and Donald C. Spencer.

This was put on a firm basis by foundational work of Kunihiko Kodaira and D. C. Spencer, after deformation techniques had received a great deal of more tentative application in the Italian school of algebraic geometry.

Deformations are numbered according to their order of formation with the letter D denoting a deformation event.

For example an F < sub > 2 </ sub > fold, with an S < sub > 2 </ sub > axial plane foliation would be the result of a D < sub > 2 </ sub > deformation.

Geomorphic evidence of deformation in the northern part of the New Madrid seismic zone Geological Survey Professional Paper 1538-R. Washington, D. C .: U. S. Department of the Interior, U. S. Geological Survey.

* Paul, J., Burgmann, R., Gaur, V. K., Bilham, R. Larson, K. M., Ananda, M. B., Jade, S., Mukal, M., Anupama, T. S .. Satyal, G., Kumar, D. 2001 The motion and active deformation of India.

& McKenzie, D., 1988 The relationship between plate motions and seismic moment tensors, and the rates of active deformation in the Mediterranean and Middle East.

* England, P. & McKenzie, D., 1982 A thin viscous sheet model for continental deformation.

From this and the force of deformation it should be possible to calculate the elastic energy of deformation which should be equal to the Af calculated from the pressure normal to the shearing face.

It is appropriate to call attention to certain thermodynamic properties of an ideal gas that are analogous to rubber-like deformation.

This is sometimes a result of the sizes of the atoms in the alloy, because larger atoms exert a compressive force on neighboring atoms, and smaller atoms exert a tensile force on their neighbors, helping the alloy resist deformation.

These defects are created during plastic deformation, such as hammering or bending, and are permanent unless the metal is recrystallized.

This deformation of the lattice causes another electron, with opposite spin, to move into the region of higher positive charge density.

* Physical deformation of the particle ( e. g., stretching ) may increase the van der Waals forces more than stabilization forces ( such as electrostatic ), resulting coagulation of colloids at certain orientations.

The internal contact forces are related to the body's deformation through constitutive equations.

Therefore, the stresses considered in continuum mechanics are only those produced by deformation of the body, sc.

The displacement of a body has two components: a rigid-body displacement and a deformation.

When analyzing the deformation or motion of solids, or the flow of fluids, it is necessary to describe the sequence or evolution of configurations throughout time.

One scholar, Ali A. Obdi, claims that imperialism inherently " involve extensively interactive regimes and heavy contexts of identity deformation, misrecognition, loss of self-esteem, and individual and social doubt in self-efficacy.

The catapult armature was attached to this drum which would be turned until enough potential energy was stored in the deformation of the spring.

The common names of illicit drugs, and the plants used to obtain them, often undergo a process similar to taboo deformation, because new terms are devised in order to discuss them secretly in the presence of others.

It occurs even more in Spanish, e. g., the deformation of names for cannabis: mota ( literally, " something that moves " on the black market ), grifa ( literally, " something coarse to the touch "), marijuana ( a female personal name, María Juana ), cáñamo ( the original Spanish name for the plant, derived from the Latin genus name Cannabis ).

Where plate boundaries occur within continental lithosphere, deformation is spread out over a much larger area than the plate boundary itself.

In the case of the San Andreas fault continental transform, many earthquakes occur away from the plate boundary and are related to strains developed within the broader zone of deformation caused by major irregularities in the fault trace ( e. g., the " Big bend " region ).

The deformation associated with this plate boundary is partitioned into nearly pure thrust sense movements perpendicular to the boundary over a wide zone to the southwest and nearly pure strike-slip motion along the Main Recent Fault close to the actual plate boundary itself.

* Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.

They also provided a driving force for crustal deformation, and a new setting for the observations of structural geology.

In the shallow crust, where brittle deformation can occur, thrust faults form, which cause deeper rock to move on top of shallower rock.