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Rheologica Acta

, Volume 10, Issue 3, pp 330–335 | Cite as

Stochastic models of relaxation phenomena

  • D. R. Axelrad
  • J. Provan
Article

Summary

The present work is concerned with simple stochastic models for the representation of the linear viscoelastic material behaviour. It is shown that such models can be employed in the same manner as the usual mechanical models. However in contrast to the mechanical models, the stochastic models are related to the microstructure of the medium by means of a material functional. In the present work the latter is shown only in a very reduced form.

Creep and relaxation functions of such materials are considered first in terms of microscopic quantities, which are random variables. By introducing the concept of a mesoscopic domain within the material sample the transition from the microscopic to the macroscopic or phenomenological representation can be achieved.

Keywords

Polymer Microstructure Stochastic Model Mechanical Model Material Sample 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

In der vorliegenden Arbeit werden einfache stochastische Modelle beschrieben. Es wird gezeigt, daß solche Modelle ebenso wie die einfachen Anordnungen von Federn und Dämpfern zur Veranschaulichung des linearen viskoelastischen Verhaltens eines Materials benutzt werden können.

Im Gegensatz zu den letzteren sind jedoch die stochastischen Modelle mit der Materialstruktur mittels einer Materialfunktion verbunden. Diese wird in einer äußerst vereinfachten Form dargestellt. Kriech- und Relaxations-Funktionen werden mittels dieser Modelle vorerst für die eingeführten mikroskopischen Variablen abgeleitet und dann mittels Einführung des Begriffes einer „mesoskopischen“ Region im. Material wird der Übergang zur makroskopischen Theorie vollzogen.

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References

  1. 1).
    Axelrad, D. R., Mechanical models of relaxation phenomena. Advances in molecular relaxation processes. Vol. 2, No. 1 (Amsterdam 1970).Google Scholar
  2. 2).
    Axelrad, D. R., Stochastic analysis of the flow of 2-phase media. 5 th Int. Congr. on Rheology. Kyoto University, Kyoto, Japan (1968) (New York 1970).Google Scholar
  3. 3).
    Axelrad, D. R. andL. G. Jaeger, Random theory of deformation in heterogeneous media. Int. Conf. on structure, solid mechs. University of Southampton, England 1968 (London 1970).Google Scholar
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    Axelrad, D. R., Probabilistic theory of aftereffects. Proc. 1st Can. Congress appl. mechs., Vol.II (Toronto 1967).Google Scholar
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    Pugachev, V. S., Theory ofRandom functions (New York 1965).Google Scholar
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    Khinchin, A. I., Mathematical foundations of statistical mechanics (New York 1949).Google Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag 1971

Authors and Affiliations

  • D. R. Axelrad
    • 1
  • J. Provan
    • 1
  1. 1.The Micromechanics of Solids LaboratoryMcGill UniversityMortrealCanada

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