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Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity

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Abstract

The results obtained previously for scalar and class P completely monotone relaxation moduli are extended to arbitrary anisotropy. It is shown for general anisotropic viscoelastic media that, if the relaxation modulus is a locally integrable completely monotone function, then the creep compliance is a Bernstein function and conversely. The elastic and equilibrium limits of the two material functions are related to each other. The relaxation modulus or its derivative can be singular at 0. A rigorous general formulation of the relaxation spectrum in an anisotropic viscoelastic medium is given. The effect of Newtonian viscosity on creep compliance is examined.

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Authors and Affiliations

  1. Department of Earth Sciences, University of Bergen, Allégaten 41, N5007, Bergen, Norway

    Andrzej Hanyga

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, 00-049 Warszawa, Świętokrzyska 21, Poland

    Małgorzata Seredyńska

Authors
  1. Andrzej Hanyga
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  2. Małgorzata Seredyńska
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Correspondence to Andrzej Hanyga.

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Hanyga, A., Seredyńska, M. Relations Between Relaxation Modulus and Creep Compliance in Anisotropic Linear Viscoelasticity. J Elasticity 88, 41–61 (2007). https://doi.org/10.1007/s10659-007-9112-6

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  • DOI: https://doi.org/10.1007/s10659-007-9112-6

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