IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3426-d1511897.html
   My bibliography  Save this article

A Comparative View of Becker, Lomnitz, and Lambert Linear Viscoelastic Models

Author

Listed:
  • Juan Luis González-Santander

    (Department de Mathematics, University of Oviedo, C Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
    These authors contributed equally to this work.)

  • Francesco Mainardi

    (Department of Physics and Astronomy, University of Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy
    These authors contributed equally to this work.)

Abstract

We compare the classical viscoelastic models due to Becker and Lomnitz with respect to a recent viscoelastic model based on the Lambert W function. We take advantage of this comparison to derive new analytical expressions for the relaxation spectrum in the Becker and Lomnitz models, as well as novel integral representations for the retardation and relaxation spectra in the Lambert model. In order to derive these analytical expressions, we have used the analytical properties of the exponential integral and the Lambert W function, as well as the Titchmarsh’s inversion formula of the Stieltjes transform. In addition, we prove some interesting inequalities by comparing the different models considered, as well as the non-negativity of the retardation and relaxation spectral functions. This means that the complete monotonicity of the rate of creep and the relaxation functions is satisfied, as required by the classical theory of linear viscoelasticity.

Suggested Citation

  • Juan Luis González-Santander & Francesco Mainardi, 2024. "A Comparative View of Becker, Lomnitz, and Lambert Linear Viscoelastic Models," Mathematics, MDPI, vol. 12(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3426-:d:1511897
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3426/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3426/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3426-:d:1511897. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.