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	<span style="font-size:1.2em;font-weight:bold;">~~A-Bild-Technik~~</span>		<span style="font-size:1.2em;font-weight:bold;">BOLTZMANN's Superposition Principle</span>
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{{Language_sel|LANG=ger|ARTIKEL=BOLTZMANN'sches Superpositionsprinzip}}
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==Laws of viscoelasticity==

BOLTZMANN's superposition principle, named after the Austrian physicist Ludwig Boltzmann (1844–1906), together with the [[Correspondence Principle|correspondence principle]] and the [[Time–Temperature Shift Law|time–temperature shift law]], is used to describe the [[Linear-viscoelastic Behaviour|linear-viscoelastic behaviour]] of [[Plastics|plastics]] [1].

==Principle of superposition for relaxation and retardation==

'''Figure 1''' illustrates these relationships using diagrams of [[Relaxation Plastics|relaxation]] and [[Creep Plastics|retardation]] experiments.

[[file:boltzmann Fig.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |BOLTZMANN's superposition principle for relaxation and retardation cases
|}

BOLTZMANN's superposition principle describes the influence of mechanical history on the material behaviour of [[Plastics|plastics]]. It states that the time-dependent effects of successive changes in the stress state add up linearly and summarily to the overall effect.

==Basic assumptions==

If the strain ''ε''1(''t'') generates a stress ''σ''1(''t'') and ''ε''2(''t'') generates the stress ''σ''2(''t''), then the sum ''ε''1(''t'') + ''ε''2(''t'') causes the total stress ''σ''1(''t'') + ''σ''2(''t'').

Conversely,

if the stress ''σ''1(''t'') produces the strain ''ε''1(''t'') and ''σ''2(''t'') produces the strain ''ε''2(''t''), then the sum ''σ''1(''t'') + ''σ''2(''t'') corresponds to the total strain ''ε''1(''t'') + ''ε''2(''t'').

The principle therefore takes into account relaxation and retardation, or the creep of plastics. The BOLTZMANN superposition principle is illustrated graphically in the schematic diagram in '''Fig. 1'''.

Based on this principle, the time-dependent [[Deformation|deformation]] caused by applied loads (and vice versa) can be determined at different times with a reasonable amount of computational effort in the area of [[Linear-viscoelastic Behaviour|linear-viscoelastic material behaviour]].

==See also==

* [[Correspondence Principle|Correspondence principle]]
* [[Time–Temperature Shift Law|Time–temperature shift law]]
* [[Relaxation Plastics|Relaxation plastics]]
* [[Creep Plastics|Creep plastics]]

'''References'''

{|
|-valign="top"
|[1]
|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. 82/83 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Büchersammlung|AMK-Library]] under A 22)
|}

[[category:Deformation]]

BOLTZMANN's Superposition Principle - Revision history

Oluschinski at 09:11, 8 January 2026