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On the growth behavior of one-dimensional acceleration waves in the linear theory of viscoelasticity

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Abstract

The growth behavior of one-dimensional accelaration waves which propagate in linear viscoelastic materials with time-dependent relaxation functions is examined. Such a time dependence arises either by linearizing the constitutive equation of a simple material about an arbitrary deformation history or by linearizing about a natural state when there is an aging process taking place in the body. Explicit results are obtained for simple types of time dependence and the results are then compared with those which follow in the usual theory of isothermal linear viscoelasticity.

Zusammenfassung

Das Wachstumsverhalten eindimensionaler Beschleunigungswellen, die sich in viskoelastischem Material mit zeitabhänginger Relaxationsfunktion fortpflanzen, wird untersucht. Eine solche Zeitabhängigkeit entsteht entweder durch Linearisierung der Zustandsgleichung eines einfachen Materials über eine beliebige Deformationsgeschichte oder für den Fall, dass im Körper ein Alterungsprozess stattfindet. Explizite Resultate werden für einfache Fälle von Zeitabhängigkeit erhalten. Die Ergebnisse werden dann mit denjenigen verglichen, die aus der üblichen Theorie isothermer linearer Viskoelastizität folgen.

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References

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Authors and Affiliations

  1. Dept. of Mathematics, and Computer Science, University of South Carolina, Columbia, USA

    Frederick Bloom

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  1. Frederick Bloom
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Bloom, F. On the growth behavior of one-dimensional acceleration waves in the linear theory of viscoelasticity. Journal of Applied Mathematics and Physics (ZAMP) 26, 361–367 (1975). https://doi.org/10.1007/BF01590549

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  • DOI: https://doi.org/10.1007/BF01590549

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