Localization in inelastic rate dependent shearing deformations

Handle URI:
http://hdl.handle.net/10754/619754
Title:
Localization in inelastic rate dependent shearing deformations
Authors:
Katsaounis, Theodoros ( 0000-0001-7387-7987 ) ; Lee, Min-Gi ( 0000-0002-1953-2547 ) ; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions. © 2016 Elsevier Ltd
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Katsaounis T, Lee M-G, Tzavaras A (2017) Localization in inelastic rate dependent shearing deformations. Journal of the Mechanics and Physics of Solids 98: 106–125. Available: http://dx.doi.org/10.1016/j.jmps.2016.08.015.
Publisher:
Elsevier BV
Journal:
Journal of the Mechanics and Physics of Solids
Issue Date:
18-Sep-2016
DOI:
10.1016/j.jmps.2016.08.015
ARXIV:
arXiv:1605.04564
Type:
Article
ISSN:
0022-5096
Sponsors:
Research supported by King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0022509616303337; https://appliedpde.kaust.edu.sa/Pages/KLT_JMPS2016.aspx; https://arxiv.org/abs/1605.04564
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKatsaounis, Theodorosen
dc.contributor.authorLee, Min-Gien
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2017-03-07T06:26:18Z-
dc.date.available2016-09-04T07:01:35Z-
dc.date.available2017-03-07T06:26:18Z-
dc.date.issued2016-09-18en
dc.identifier.citationKatsaounis T, Lee M-G, Tzavaras A (2017) Localization in inelastic rate dependent shearing deformations. Journal of the Mechanics and Physics of Solids 98: 106–125. Available: http://dx.doi.org/10.1016/j.jmps.2016.08.015.en
dc.identifier.issn0022-5096en
dc.identifier.doi10.1016/j.jmps.2016.08.015en
dc.identifier.urihttp://hdl.handle.net/10754/619754-
dc.description.abstractMetals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions. © 2016 Elsevier Ltden
dc.description.sponsorshipResearch supported by King Abdullah University of Science and Technology (KAUST).en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0022509616303337en
dc.relation.urlhttps://appliedpde.kaust.edu.sa/Pages/KLT_JMPS2016.aspxen
dc.relation.urlhttps://arxiv.org/abs/1605.04564en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of the Mechanics and Physics of Solids, 17 September 2016. DOI: 10.1016/j.jmps.2016.08.015en
dc.subjectHadamard instabilityen
dc.subjectShear bandsen
dc.subjectShear localizationen
dc.subjectStrain-rate sensitivityen
dc.subjectTuring instabilityen
dc.titleLocalization in inelastic rate dependent shearing deformationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of the Mechanics and Physics of Solidsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greeceen
dc.contributor.institutionInstitute of Applied and Computational Mathematics, FORTH, Heraklion, Greeceen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1605.04564en
kaust.authorKatsaounis, Theodorosen
kaust.authorLee, Min-Gien
kaust.authorTzavaras, Athanasiosen

Version History

VersionItem Editor Date Summary
2 10754/619754grenzdm2017-03-07 06:23:58.184Article published with DOI.
1 10754/619754.1Theodoros Katsaounis2016-09-04 07:01:35.0
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