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dc.contributor.authorLee, Min-Gien
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2016-11-13T08:22:10Z
dc.date.available2016-11-13T08:22:10Z
dc.date.issued2016-07-31
dc.identifier.urihttp://hdl.handle.net/10754/621820.1
dc.description.abstractShear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to reveal the onset of localization into shear bands using a simple model developed from viscoplasticity. We exploit the properties of scale invariance of the model to construct a family of self-similar focusing solutions that capture the nonlinear mechanism of shear band formation. The key step is to de-singularize a reduced system of singular ordinary differential equations and reduce the problem into the construction of a heteroclinic orbit for an autonomous system of three first-order equations. The associated dynamical system has fast and slow time scales, forming a singularly perturbed problem. The geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincar\'{e}-Bendixson theorem to construct a heteroclinic orbit.en
dc.description.sponsorshipThis research was supported by King Abdullah University of Science and Technology (KAUST).en
dc.language.isoenen
dc.relation.urlhttps://arxiv.org/abs/1608.00198en
dc.titleExistence of localizing solutions in plasticity via the geometric singular perturbation theoryen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical, Mathematical Sciences & Engineering Divisionen
dc.eprint.versionPre-printen
dc.identifier.arxivid1608.00198
kaust.personLee, Min-Gi
kaust.personTzavaras, Athanasios


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