Rheological implications of completely monotone fading memory
| dc.contributor.author | Anderssen, R. S. | |
| dc.contributor.author | Loy, R. J. | |
| dc.date.accessioned | 2015-10-19T04:15:33Z | |
| dc.date.available | 2015-10-19T04:15:33Z | |
| dc.date.issued | 2002-11 | |
| dc.date.updated | 2015-12-12T09:28:35Z | |
| dc.description.abstract | In the constitutive equation modeling of a (linear) viscoelastic material, the “fading memory” of the relaxation modulusG(t) is a fundamental concept that dates back to Boltzmann [Ann. Phys. Chem. 7, 624 (1876)]. There have been various proposals that range from the experimental and pragmatic to the theoretical about how fading memory should be defined. However, if, as is common in the rheological literature, one assumes that G(t) has the following relaxation spectrum representation: G(t)=∫₀∞ exp(−t/τ)[H(τ)/τ]dτ, t > 0, then it follows automatically that G(t) is a completely monotone function. Such functions have quite deep mathematical properties, that, in a rheological context, spawn interesting and novel implications. For example, because the set of completely monotone functions is closed under positive linear combinations and products, it follows that the dynamics of a linear viscoelastic material, under appropriate stress–strain stimuli, will involve a simultaneous mixture of different molecular interactions. In fact, it has been established experimentally, for both binary and polydisperse polymeric systems, that the dynamics can simultaneously involve a number of different molecular interactions such as the Rouse, double reptation and/or diffusion, [W. Thimm et al., J. Rheol., 44, 429 (2000); F. Léonardi et al., J. Rheol. 44, 675 (2000)]. The properties of completely monotone functions either yield new insight into modeling of the dynamics of real polymers, or they call into question some of the key assumptions on which the current modeling is based, such as the linearity of the Boltzmann model of viscoelasticity and/or the relaxation spectrum representation for the relaxation modulusG(t). If the validity of the relaxation spectrum representation is accepted, the resulting mathematical properties that follow from the complete monotonicity of G(t) allows one to place the classical relaxation model of Doi and Edwards [M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2 74, 1789 (1978)], as a linear combination of exp(−t/τ*) relaxation processes, each with a characteristic relaxation time τ*, on a more general and rigorous footing. | |
| dc.identifier.issn | 0148-6055 | en_AU |
| dc.identifier.uri | http://hdl.handle.net/1885/15968 | |
| dc.publisher | American Institute of Physics (AIP) | |
| dc.rights | http://www.sherpa.ac.uk/romeo/issn/0148-6055..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 19/10/15). Copyright © 2002 by The Society of Rheology, Inc. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Rheology and may be found at https://doi.org/10.1122/1.1514203 | |
| dc.source | Journal of Rheology | |
| dc.subject | Keywords: Polymers; Relaxation processes; Strain; Stress analysis; Viscoelasticity; Fading memory; Rheology | |
| dc.title | Rheological implications of completely monotone fading memory | |
| dc.type | Journal article | |
| local.bibliographicCitation.issue | 6 | en_AU |
| local.bibliographicCitation.lastpage | 1472 | en_AU |
| local.bibliographicCitation.startpage | 1459 | en_AU |
| local.contributor.affiliation | Anderssen, Robert S, CSIRO Mathematical and Information Sciences, Australia | en_AU |
| local.contributor.affiliation | Loy, Richard, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Department of Mathematics, The Australian National University | en_AU |
| local.contributor.authoremail | Rick.Loy@anu.edu.au | en_AU |
| local.contributor.authoruid | u7000666 | en_AU |
| local.description.notes | Imported from ARIES | en_AU |
| local.description.refereed | Yes | |
| local.identifier.absfor | 010399 | en_AU |
| local.identifier.ariespublication | MigratedxPub23969 | en_AU |
| local.identifier.citationvolume | 46 | en_AU |
| local.identifier.doi | 10.1122/1.1514203 | en_AU |
| local.identifier.scopusID | 2-s2.0-0036870531 | |
| local.identifier.uidSubmittedBy | u3488905 | en_AU |
| local.publisher.url | https://www.aip.org/ | en_AU |
| local.type.status | Published Version | en_AU |
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