{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T06:46:58Z","timestamp":1763016418556},"reference-count":24,"publisher":"Elsevier BV","issue":"11","license":[{"start":{"date-parts":[[2003,11,1]],"date-time":"2003-11-01T00:00:00Z","timestamp":1067644800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Signal Processing"],"published-print":{"date-parts":[[2003,11]]},"DOI":"10.1016\/s0165-1684(03)00187-7","type":"journal-article","created":{"date-parts":[[2003,9,12]],"date-time":"2003-09-12T07:48:17Z","timestamp":1063352897000},"page":"2345-2357","source":"Crossref","is-referenced-by-count":54,"title":["Constitutive equations for polymer viscoelasticity derived from hierarchical models in cases of failure of time\u2013temperature superposition"],"prefix":"10.1016","volume":"83","author":[{"given":"Nicole","family":"Heymans","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0165-1684(03)00187-7_BIB1","doi-asserted-by":"crossref","first-page":"6269","DOI":"10.1016\/S0032-3861(98)00168-2","article-title":"Application of fractional calculus to viscoelastic behaviour modelling and to the physical ageing phenomenon in glassy amorphous polymers","volume":"39","author":"Alcoutlabi","year":"1998","journal-title":"Polymer"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB2","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1122\/1.549724","article-title":"A theoretical basis for the application of fractional calculus to viscoelasticity","volume":"27","author":"Bagley","year":"1983","journal-title":"J. Rheol."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB3","first-page":"149","article-title":"A deformation model of polycarbonate extended to the loss curve in the \u03b1 transition range","volume":"18","author":"Bauwens","year":"1992","journal-title":"Plast. Rubber Compos. Process. Appl."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB4","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/BF00396182","article-title":"On the admissibility criteria for linear viscoelastic kernels","volume":"32","author":"Beris","year":"1993","journal-title":"Rheol. Acta."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB5","series-title":"Rheological modelling: Thermodynamical and statistical approaches","first-page":"321","article-title":"Relaxation functions of rheological constitutive equations with fractional derivatives: thermodynamical constraints","volume":"Vol. 381","author":"Friedrich","year":"1991"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB6","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF01134604","article-title":"Relaxation and retardation functions of the Maxwell model with fractional derivatives","volume":"30","author":"Friedrich","year":"1991","journal-title":"Rheol. Acta."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB7","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0377-0257(93)85052-C","article-title":"Mechanical stress relaxation in polymers","volume":"46","author":"Friedrich","year":"1993","journal-title":"J. Non-Newtonian Fluid Mech."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF00418328","article-title":"Generalized Cole\u2013Cole behavior and its rheological relevance","volume":"31","author":"Friedrich","year":"1992","journal-title":"Rheol. Acta."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB9","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.1007\/BF00664721","article-title":"Linear viscoelastic behaviour of complex materials","volume":"272","author":"Friedrich","year":"1994","journal-title":"Colloid Polym. Sci."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB10","doi-asserted-by":"crossref","unstructured":"C. Friedrich, H. Schiessel, A. Blumen, Constitutive behaviour modeling and fractional derivatives, Advances in the Flow and Rheology of Non-Newtonian Fluids, Elsevier, Amsterdam, 1999, pp. 429\u2013466.","DOI":"10.1016\/S0169-3107(99)80038-0"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB11","doi-asserted-by":"crossref","first-page":"6426","DOI":"10.1021\/ma00024a009","article-title":"Fractional integral operators and fox functions in the theory of viscoelasticity","volume":"24","author":"Gl\u00f6ckle","year":"1991","journal-title":"Macromolecules"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB12","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/BF00654010","article-title":"A quantitative model describing physical aging in isotactic polypropylenes","volume":"273","author":"Hellinckx","year":"1995","journal-title":"Colloid Polym. Sci."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB13","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/s003960050060","article-title":"Mechanical behaviour of isotactic polypropylenes in the lower and upper glass transition ranges. 1. Linear behaviour","volume":"275","author":"Hellinckx","year":"1997","journal-title":"Colloid Polym. Sci."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB14","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1007\/BF00369000","article-title":"Hierarchical models for viscoelasticity","volume":"35","author":"Heymans","year":"1996","journal-title":"Rheol. Acta."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB15","unstructured":"N. Heymans, Modelling non-linear and time-dependent behaviour of viscoelastic materials using hierarchical models, 5th European Rheology Conference, Portoroz, Slovenia, 6\u201311 September 1998. Progr. Trends Rheol. 5 (1998) 100\u2013101."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB16","unstructured":"N. Heymans, Properties of hierarchical models for non-linear viscoelastic behaviour, CanCNSM first Canadian Conference on Nonlinear Solid Mechanics, Victoria, BC, Canada, 16\u201320 June 1999, pp. 255\u2013263."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB17","unstructured":"N. Heymans, Connection between threshold yield stress and double yield in semi-crystalline polymers, 11th International Conference on Deformation, Yield and Fracture of Polymers, Cambridge, U.K., 10\u201313 April 2000, pp. 109\u2013112."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB18","doi-asserted-by":"crossref","unstructured":"N. Heymans, Implementation of fractional calculus using hierarchical models\u2014application to the terminal transition of a complex polymer, Paper VIB-48396, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois USA, September 2\u20136, 2003.","DOI":"10.1115\/DETC2003\/VIB-48396"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB19","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/BF00437306","article-title":"Fractal rheological models and fractional differential equations for viscoelastic behaviour","volume":"33","author":"Heymans","year":"1994","journal-title":"Rheol. Acta."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB20","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1115\/1.3167616","article-title":"Applications of fractional calculus to the theory of viscoelasticity","volume":"51","author":"Koeller","year":"1984","journal-title":"J. Appl. Mech."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB21","series-title":"The Fractional Calculus","author":"Oldham","year":"1974"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB22","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/0032-3861(89)90213-9","article-title":"Mechanical relaxation in isotactic polypropylene","volume":"30","author":"Read","year":"1989","journal-title":"Polymer"},{"key":"10.1016\/S0165-1684(03)00187-7_BIB23","doi-asserted-by":"crossref","first-page":"5057","DOI":"10.1088\/0305-4470\/26\/19\/034","article-title":"Hierarchical analogues to fractional relaxation equations","volume":"26","author":"Schiessel","year":"1993","journal-title":"J. Phys. A: Math. Gen."},{"key":"10.1016\/S0165-1684(03)00187-7_BIB24","series-title":"The Phenomenological Theory of Linear Viscoelastic Behavior. An Introduction","author":"Tschoegl","year":"1989"}],"container-title":["Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168403001877?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168403001877?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,24]],"date-time":"2019-02-24T14:51:12Z","timestamp":1551019872000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165168403001877"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":24,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S0165168403001877"],"URL":"https:\/\/doi.org\/10.1016\/s0165-1684(03)00187-7","relation":{},"ISSN":["0165-1684"],"issn-type":[{"value":"0165-1684","type":"print"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}