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dc.contributor.authorDestrade, Michel
dc.contributor.authorSaccomandi, Giuseppe
dc.contributor.authorSgura, Ivonne
dc.date.accessioned2017-04-25T08:36:44Z
dc.date.issued2017-02-08
dc.identifier.citationDestrade, Michel, Saccomandi, Giuseppe, & Sgura, Ivonne. (2017). Methodical fitting for mathematical models of rubber-like materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 473(2198). doi: 10.1098/rspa.2016.0811en_IE
dc.identifier.issn1471-2946
dc.identifier.urihttp://hdl.handle.net/10379/6482
dc.description.abstractA great variety of models can describe the nonlinear response of rubber to uniaxial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney plot transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the 'upturn' of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak nonlinear elasticity theory and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of nonlinear elasticity is much more robust that seemed at first sight.en_IE
dc.formatapplication/pdfen_IE
dc.language.isoenen_IE
dc.publisherThe Royal Society Publishingen_IE
dc.relation.ispartofProceedings Of The Royal Society A-Mathematical Physical And Engineering Sciencesen
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Ireland
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/ie/
dc.subjectNonlinear elasticityen_IE
dc.subjectConstitutive equationsen_IE
dc.subjectRubberen_IE
dc.subjectConstitutive modelsen_IE
dc.subjectHyperelastic modelsen_IE
dc.subjectGhent modelsen_IE
dc.subjectElasticityen_IE
dc.subjectShearen_IE
dc.subjectDeformationen_IE
dc.subjectMechanicsen_IE
dc.subjectNetworksen_IE
dc.subjectConstitutive equationsen_IE
dc.titleMethodical fitting for mathematical models of rubber-like materialsen_IE
dc.typeArticleen_IE
dc.date.updated2017-04-13T12:51:20Z
dc.identifier.doi10.1098/rspa.2016.0811
dc.local.publishedsourcehttp://dx.doi.org/10.1098/rspa.2016.0811en_IE
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|
dc.description.embargo2018-02-08
dc.internal.rssid12329294
dc.local.contactMichel Destrade, Room Adb-1002, Áras De Brun, School Of Mathematics, Nui Galway. 2344 Email: michel.destrade@nuigalway.ie
dc.local.copyrightcheckedNo
dc.local.versionACCEPTED
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