Emergence of coherent localized structures in shear deformations of temperature dependent fluids

Handle URI:
http://hdl.handle.net/10754/583109
Title:
Emergence of coherent localized structures in shear deformations of temperature dependent fluids
Authors:
Katsaounis, Theodoros ( 0000-0001-7387-7987 ) ; Olivier, Julien; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonian fluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states - in the form of similarity solutions - that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in \cite{KT}.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
Issue Date:
25-Nov-2016
DOI:
10.1007/s00205-016-1071-2
ARXIV:
arXiv:1411.6131
Type:
Article
ISSN:
0003-9527
Sponsors:
Research partially supported by the EU FP7-REGPOT project "Archimedes Center for Modeling, Analysis and Computation" and the "DIKICOMA" project of the Hellenic Secretariat of Research and Technology. Part of this work was completed at the Department of Applied Mathematics, University of Crete, Greece.
Additional Links:
http://arxiv.org/abs/1411.6131
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorKatsaounis, Theodorosen
dc.contributor.authorOlivier, Julienen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2016-11-27T08:52:46Z-
dc.date.available2015-12-02T12:32:21Zen
dc.date.available2016-11-27T08:52:46Z-
dc.date.issued2016-11-25-
dc.identifier.issn0003-9527en
dc.identifier.doi10.1007/s00205-016-1071-2en
dc.identifier.urihttp://hdl.handle.net/10754/583109-
dc.description.abstractShear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonian fluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states - in the form of similarity solutions - that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in \cite{KT}.en
dc.description.sponsorshipResearch partially supported by the EU FP7-REGPOT project "Archimedes Center for Modeling, Analysis and Computation" and the "DIKICOMA" project of the Hellenic Secretariat of Research and Technology. Part of this work was completed at the Department of Applied Mathematics, University of Crete, Greece.en
dc.language.isoenen
dc.publisherSpringer Natureen
dc.relation.urlhttp://arxiv.org/abs/1411.6131en
dc.titleEmergence of coherent localized structures in shear deformations of temperature dependent fluidsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.eprint.versionPost-printen
dc.contributor.institutionInstitute of Applied and Computational Mathematics, FORTH, Heraklion 71110, Greeceen
dc.contributor.institutionCentre de Math ematiques et Informatique, Aix-Marseille Universite, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, Franceen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1411.6131-
kaust.authorKatsaounis, Theodorosen
kaust.authorTzavaras, Athanasiosen

Version History

VersionItem Editor Date Summary
2 10754/583109grenzdm2016-11-27 08:26:10.6Final accepted manuscript received by email.
1 10754/583109.1wangh0e2015-12-02 12:32:21.0
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