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...''. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression. * [[force]] — [[deformation (engineering)|deformation]] ...

..."W") is a measure of the relative importance of [[Deformation (mechanics)|deformation]] and [[rotation]] at a given point. It is calculated as the sum of the squ [[Category:Continuum mechanics]] ...

...change in diameter of a circular bar of a material to its diameter due to deformation in the longitudinal direction. It occurs when under the action of a [[longi * [[Deformation (mechanics)]] ...

...]] behaviour.<ref>{{cite journal|last1=Yeoh|first1=O. H.|title=Analysis of deformation and fracture of 'pure shear'rubber testpiece|journal=Plastics, Rubber and C The deformation gradient for pure shear is given by: ...

...int is determined only by the current state of [[deformation (engineering)|deformation]] with respect to an arbitrary reference configuration.<ref name=Ogden>R. W ...nfinitesimal neighborhood of the point in question, without regard for the deformation or motion of the rest of the material. It also implies that body forces (su ...

...ticity]] '''Clapeyron's theorem''' states that the [[potential energy]] of deformation of a body, which is in equilibrium under a given load, is equal to half the ...the pulling force is&nbsp;''F''. By the theorem, the potential energy of deformation in the spring is given by: ...

{{Continuum mechanics|cTopic=[[Solid mechanics]]}} ...nomial in the two invariants <math>I_1,I_2</math> of the left Cauchy-Green deformation tensor. ...

...n a body. This state of strain is achieved when the [[displacement field (mechanics)|displacement]]s in the body are zero in the plane of interest but nonzero For an [[isotropic]], [[Deformation (engineering)#Elastic_deformation|linear elastic]] material, the [[stress ( ...

...a load to a material point can lead to arbitrary [[deformation (mechanics)|deformation]]s at that material point unless an additional length or time scale is spec ...uniqueness and stability in elastic-plastic solids|journal=Journal of the Mechanics and Physics of Solids|volume=6|issue=3|pages=236–249|doi=10.1016/0022-5096( ...

In the case of [[finite deformation tensor|finite deformations]], the '''Piola–Kirchhoff stress tensors''' (nam ...example, the Cauchy Stress tensor is variant to a pure rotation, while the deformation strain tensor is invariant; thus creating problems in defining a constituti ...

...4/1.3538540 |url=https://meridian.allenpress.com/rct/article/64/1/57/91469/Deformation-Index-Concept-for-Hysteretic-Energy |access-date=4 August 2022}}</ref> or [ ...aried, the process is said to be load controlled. Between the extremes of deformation and load control, there is a spectrum of intermediate modes of control incl ...

{{Continuum mechanics|cTopic=[[Solid mechanics]]}} ...ingularity|singularity]] when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value <math>I_m</math>. ...

...stress can be defined:<ref>J. Bonet and R. W. Wood, ''Nonlinear Continuum Mechanics for Finite Element Analysis'', Cambridge University Press.</ref><ref>R. W. ...symbol{F}</math> is the [[Finite strain theory#Deformation gradient tensor|deformation gradient tensor]], <math>J</math> is its determinant. ...

...can lead to [[fracture|fracturing]] or [[Deformation (engineering)|plastic deformation]] depending on the other variables of heating, which include material types [[File:Rail buckle.jpg|thumb|Example of deformation induced by thermal stress on the rails]] ...

{{Continuum mechanics|cTopic=[[Solid mechanics]]}} ...other [[polymer]]ic substances. This model is based on the [[statistical mechanics]] of a material with a cubic [[representative volume element]] containing e ...

[[File:Biegeanimation 2D.gif|300px|thumb|Plastic deformation of a thin metal sheet.]] ...ty)|flow rule]] exists that can be used to determine the amount of plastic deformation in the material. ...

....<ref>Tsallis, C. (2009) "Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years", ''Braz. J. Phys'', 39, 337–356</ref> Similarly ...distributions have been applied to problems in the fields of [[statistical mechanics]], [[geology]], [[anatomy]], [[astronomy]], [[economics]], [[finance]], and ...

In [[mechanics]] and [[geodynamics]], a '''critical taper''' is the equilibrium angle made ...cal taper until such a point as the high angle of the taper makes internal deformation more difficult than sliding along the base. If the basal décollement deform ...

In [[continuum mechanics]], a '''hypoelastic material'''<ref>Truesdell (1963).</ref> is an [[elastic ...ifford | last2=Noll|first2=Walter | title=The Non-linear Field Theories of Mechanics | year=2004 | publisher=Springer-Verlag|location=Berlin Heidelberg New York ...

...ity function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called the '''reduced [[Polynomial ( ...urai, A. P. S., 2006, "Deflections of a rubber membrane", ''Journal of the Mechanics and Physics of Solids'', vol. 54, no. 6, pp. 1093-1119.</ref> This model i ...