Calculation of the Relaxation Modulus in the Andrade Model by Using the Laplace Transform

Juan Luis González-Santander, Giorgio Spada, Francesco Mainardi, Alexander Apelblat

Research output: Contribution to journalArticlepeer-review

Abstract

In the framework of the theory of linear viscoelasticity, we derive an analytical expression of the relaxation modulus in the Andrade model (Formula presented.) for the case of rational parameter (Formula presented.) in terms of Mittag–Leffler functions from its Laplace transform (Formula presented.). It turns out that the expression obtained can be rewritten in terms of Rabotnov functions. Moreover, for the original parameter (Formula presented.) in the Andrade model, we obtain an expression in terms of Miller-Ross functions. The asymptotic behaviours of (Formula presented.) for (Formula presented.) and (Formula presented.) are also derived applying the Tauberian theorem. The analytical results obtained have been numerically checked by solving the Volterra integral equation satisfied by (Formula presented.) by using a successive approximation approach, as well as computing the inverse Laplace transform of (Formula presented.) by using Talbot’s method.

Original languageEnglish
Article number439
JournalFractal and Fractional
Volume8
Issue number8
DOIs
StatePublished - 1 Aug 2024

Keywords

  • Andrade model
  • Laplace transform
  • Mittag-Leffler function
  • relaxation modulus in linear viscoelasticity

ASJC Scopus subject areas

  • Analysis
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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