Show simple item record

dc.contributor.authorLee, Min-Gi
dc.contributor.authorKatsaounis, Theodoros
dc.contributor.authorTzavaras, Athanasios
dc.date.accessioned2019-03-20T13:30:37Z
dc.date.available2019-02-24T07:16:38Z
dc.date.available2019-03-20T13:30:37Z
dc.date.issued2019-03-04
dc.identifier.citationLee M-G, Katsaounis T, Tzavaras AE (2019) Localization in Adiabatic Shear Flow Via Geometric Theory of Singular Perturbations. Journal of Nonlinear Science. Available: http://dx.doi.org/10.1007/s00332-019-09538-3.
dc.identifier.issn0938-8974
dc.identifier.issn1432-1467
dc.identifier.doi10.1007/s00332-019-09538-3
dc.identifier.urihttp://hdl.handle.net/10754/631130
dc.description.abstractWe study localization occurring during high-speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition between Hadamard instability (caused by softening response) and the stabilizing effects of strain rate hardening. We consider a hyperbolic–parabolic system that expresses the above mechanism and construct self-similar solutions of localizing type that arise as the outcome of the above competition. The existence of self-similar solutions is turned, via a series of transformations, into a problem of constructing a heteroclinic orbit for an induced dynamical system. The dynamical system is in four dimensions but has a fast–slow structure with respect to a small parameter capturing the strength of strain rate hardening. Geometric singular perturbation theory is applied to construct the heteroclinic orbit as a transversal intersection of two invariant manifolds in the phase space.
dc.description.sponsorshipThe authors thank Prof. Peter Szmolyan for valuable discussions on the use of geometric singular perturbation theory.
dc.publisherSpringer Nature
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs00332-019-09538-3
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s00332-019-09538-3
dc.subjectGeometric theory of singular perturbations
dc.subjectLocalization
dc.subjectSelf-similarity
dc.subjectShear bands
dc.titleLocalization in Adiabatic Shear Flow Via Geometric Theory of Singular Perturbations
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Nonlinear Science
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, Kyungpook National University, Daegu, , South Korea
dc.contributor.institutionDepartment of Mathematics and Applied Mathematics, University of Crete, Heraklion, , Greece
dc.contributor.institutionInstitute of Applied and Computational Mathematics, FORTH, Heraklion, , Greece
dc.identifier.arxivid1707.05283
kaust.personKatsaounis, Theodoros
kaust.personTzavaras, Athanasios
refterms.dateFOA2020-03-04T00:00:00Z


Files in this item

Thumbnail
Name:
ssband.pdf
Size:
652.6Kb
Format:
PDF
Description:
Accepted Manuscript

This item appears in the following Collection(s)

Show simple item record

VersionItemEditorDateSummary

*Selected version