On Hadamard stability and dissipative stability of the molecular stress function model of non-linear viscoelasticity

Voyiatzis, E; Tsenoglou, CJ; Boudouvis, AG

dc.contributor.author	Voyiatzis, E	en
dc.contributor.author	Tsenoglou, CJ	en
dc.contributor.author	Boudouvis, AG	en
dc.date.accessioned	2014-03-01T01:31:32Z
dc.date.available	2014-03-01T01:31:32Z
dc.date.issued	2009	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19810
dc.subject	Constitutive equation	en
dc.subject	Dissipative stability	en
dc.subject	Hadamard stability	en
dc.subject	Molecular stress function (MSF) theory	en
dc.subject	Non-linear viscoelasticity	en
dc.subject	Simple elongation	en
dc.subject	Simple shear	en
dc.subject.classification	Mechanics	en
dc.subject.other	Dissipative stability	en
dc.subject.other	Hadamard stability	en
dc.subject.other	Molecular stress function (MSF) theory	en
dc.subject.other	Non-linear viscoelasticity	en
dc.subject.other	Simple elongation	en
dc.subject.other	Simple shear	en
dc.subject.other	Constitutive equations	en
dc.subject.other	Elasticity	en
dc.subject.other	Elongation	en
dc.subject.other	Energy dissipation	en
dc.subject.other	Number theory	en
dc.subject.other	Strain	en
dc.subject.other	Stresses	en
dc.subject.other	Thermodynamic stability	en
dc.subject.other	Three dimensional	en
dc.subject.other	Viscoelasticity	en
dc.subject.other	Viscosity	en
dc.subject.other	Stability criteria	en
dc.title	On Hadamard stability and dissipative stability of the molecular stress function model of non-linear viscoelasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijnonlinmec.2009.03.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijnonlinmec.2009.03.002	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We study the stability characteristics of the molecular stress function (MSF) model, i.e.. a molecular constitutive theory for stress that extends the original Doi-Edwards model for linear polymers to the case of branched polymers, by repeating the assumption that the tension in the deformed chain is equal to its equilibrium value. We derive analytical, closed-form conditions for Hadamard stability under general 3-D high-frequency, short-amplitude wave disturbances in bi-quadratic form, which reduce to simple algebraic criteria for the cases of 1-D and 2-D disturbances. Application of the derived conditions in the case of general biaxial extension, which provides a simplified description of many processes encountered in industry and nature, shows that the MSF is Hadamard unstable for strains beyond 2. This casts doubts on its ability in predicting correct elastic response under rapid extensional deformations. The region of instability widens with the strengthening of network connectivity or the alignment strength of the flow. Dissipative stability of the MSF is examined using two necessary criteria: the first and less restrictive criterion requires the stress to be monotonically and unboundedly increasing function of strain in uniaxial elongation and simple shear. The second criterion requires the free energy and the rate of energy dissipation to be bounded functions of deformation. We find that while MSF satisfies the first stability criterion, violates the second, thus revealing thermodynamic inconsistencies in formulating the dissipative terms of the constitutive equation. (C) 2009 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.doi	10.1016/j.ijnonlinmec.2009.03.002	en
dc.identifier.isi	ISI:000268362200002	en
dc.identifier.volume	44	en
dc.identifier.issue	7	en
dc.identifier.spage	727	en
dc.identifier.epage	734	en