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{{Language_sel|LANG=ger|ARTIKEL=Korrespondenzprinzip}}
{{PSM_Infobox}}
Correspondence principle
__FORCETOC__

==Classification==

The correspondence principle is derived from [[BOLTZMANN's Superposition Principle|BOLTZMANN's superposition principle]]. It provides the important practical statement that the solutions available from elasticity theory may be used in the [[Linear-viscoelastic Behaviour|linear-viscoelastic range]]. The prerequisite for this is that the viscoelastic [[Deformation|deformations]] in [[Plastics|plastics]] used in construction are very small. Since these solutions form the basis of all [[Strength|strength]] calculations, this greatly facilitates the use of plastics.

==Fundamentals Correspondence principle==

Instead of the stresses ''σ'', the time-dependent stress function ''σ''(''t'') is used; instead of the deformation ''ε'', the time-dependent deformation ''ε''(''t'') is used; and instead of the [[Elastic Modulus|modulus of elasticity]], the relaxation modulus ''E''r(''t'') or the creep modulus (see: [[Creep Behaviour – Determination|creep behaviour determination]]) is used. However, instead of the relaxation or creep modulus, the reciprocal value, the compliance ''C''(''t'') = 1/''E''r(''t'') (''C''...compliance), is usually used.

This also applies, of course, to every other modulus ([[Shear Modulus|shear modulus]] and [[Energy Elasticity|modulus of compressibility]]), every other stress and every other [[Deformation|deformation]]. The time-dependent variables are interrelated by the relationships known from [[Elasticity|elasticity theory]], whereby the time dependence of [[Poisson's Ratio|transverse contraction]] must also be taken into account.

==Time and temperature dependence of modulus and Poisson's ratio==

The following examples show the time and temperature dependence of the [[Elastic Modulus|elastic modulus]] of acrylonitrile butadiene styrene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: ABS) and the time dependence of the Poisson's ratio using poly(methyl methacrylate) ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PMMA) as an example.

[[file:korrespondenz1.jpg|400px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Time and temperature dependence of the modulus of elasticity for ABS according to [[Menges, Georg|Menges]]
|}

[[file:Correspondance_2.jpg|400px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |[[Poisson's Ratio|Poisson's ratio]] as a function of [[Strain Rate Basics|strain rate]] ε˙ of PMMA under [[Uniaxial Stress State|uniaxial]] [[Deformation|deformation]] according to [[Menges, Georg|Menges]]
|}

==See also==

* [[Elasticity]]
* [[Linear-viscoelastic Behaviour|Linear-viscoelastic behaviour]]
* [[BOLTZMANN's Superposition Principle|BOLTZMANN's superposition principle]]
* [[Time–Temperature Shift Law|Time–temperature shift law]]

'''References'''

* [[Menges, Georg|Menges, G.]]: Werkstoffkunde Kunststoffe. 3rd, completely revised and expanded edition, Carl Hanser, Munich Vienna (1990) p. 121, (ISBN 978-3-446-15612-8; see [[AMK-Büchersammlung|AMK-Library]] under G 11)
* Lüpke, T.: Fundamental Principles of Mechanical Behavior. In: [[Grellmann, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 84 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-806-5; see [[AMK-Büchersammlung|AMK-Library]] under A 22)

[[category: Thermoanalytical Methods]]

Correspondence Principle - Revision history