{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:04:43Z","timestamp":1771466683517,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The mechanical behaviour of materials can be described by a phenomenological relationship that binds strain to stress, by the complex modulus function: M(\u03c9), which represents the frequency response of the medium in which a transverse mechanical wave is propagated. From the experimental measurements of the internal friction obtained when varying the frequency of a transverse mechanical wave, the parameters that characterize the complex module are determined. The internal friction or loss tangent is bound to the dissipation of the specific mechanical energy. The non-equilibrium thermodynamics theory leads to a general description of irreversible phenomena such as relaxation and viscosity that can coexist in a material. Through the state variables introduced by Ciancio and Kluitenberg, and applying the fractional calculation due to a particular memory mechanism, a model of a viscoanelastic medium is obtained in good agreement with the experimental results.<\/jats:p>","DOI":"10.3390\/axioms12030243","type":"journal-article","created":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T02:01:51Z","timestamp":1677549711000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Fractional Rheological Model of Viscoanelastic Media"],"prefix":"10.3390","volume":"12","author":[{"given":"Armando","family":"Ciancio","sequence":"first","affiliation":[{"name":"Department of Biomedical and Dental Sciences and Morphofunctional Imaging (BIOMORF), University of Messina, Via Consolare Valeria c\/o A.O.U. Policlinico \u2019G.Martino\u2019, 98126 Messina, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1387-6103","authenticated-orcid":false,"given":"Vincenzo","family":"Ciancio","sequence":"additional","affiliation":[{"name":"Accademia Peloritana dei Pericolanti, Piazza S. Pugliatti 1, 98122 Messina, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7619-2155","authenticated-orcid":false,"given":"Bruno Felice Filippo","family":"Flora","sequence":"additional","affiliation":[{"name":"Azienda Ospedaliera \u201cPapardo\u201d, Viale F. Stagno d\u2019Alcontres 34, 98158 Messina, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/0031-8914(62)90064-2","article-title":"On rheology and thermodynamics of irreversible processes","volume":"28","author":"Kluitenberg","year":"1962","journal-title":"Physica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/0031-8914(62)90110-6","article-title":"A note on the thermodynamics of Maxwell bodies, Kelvin bodies (Voigt bodies), and fluids","volume":"28","author":"Kluitenberg","year":"1962","journal-title":"Physica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/S0031-8914(63)80222-0","article-title":"On the thermodynamics of viscosity and plasticity","volume":"29","author":"Kluitenberg","year":"1963","journal-title":"Physica"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0031-8914(67)90064-X","article-title":"On heat dissipation due to irreversible mechanical phenomena in continuous media","volume":"35","author":"Kluitenberg","year":"1967","journal-title":"Physica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/0031-8914(68)90002-5","article-title":"A thermodynamic derivation of the stress\u2013strain relations for burgers media and related substances","volume":"38","author":"Kluitenberg","year":"1968","journal-title":"Physica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0378-4371(78)90221-2","article-title":"On linear dynamical equations of state for isotropic media I: General formalism","volume":"93","author":"Kluitenberg","year":"1978","journal-title":"Phys. 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