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dc.contributor.author
Ammari, Habib
dc.contributor.author
Kang, Hyeonbae
dc.contributor.author
Kim, Do Wan
dc.contributor.author
Yu, Sanghyeon
dc.date.accessioned
2020-08-27T12:08:30Z
dc.date.available
2020-08-27T09:45:29Z
dc.date.available
2020-08-27T12:08:30Z
dc.date.issued
2020-03
dc.identifier.uri
http://hdl.handle.net/20.500.11850/432895
dc.description.abstract
When two inclusions with high contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress concentration in the two-dimensional Stokes flow when inclusions are the two-dimensional cross sections of circular cylinders of the same radii and the background velocity field is linear. We construct two vector-valued functions which completely capture the singular behavior of the stress and derive an asymptotic representation formula for the stress in terms of these functions as the distance between the two cylinders tends to zero. We then show, using the representation formula, that the stress always blows up by proving that either the pressure or the shear stress component of the stress tensor blows up. The blow-up rate is shown to be one over the square root of the distance between the two cylinders.
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.subject
Stress concentration
en_US
dc.subject
Blow-up
en_US
dc.subject
Stokes flow
en_US
dc.subject
Stokes system
en_US
dc.subject
singular functions
en_US
dc.subject
Bi-polar coordinates
en_US
dc.title
Quantitative estimates for stress concentration of the Stokes flow between adjacent circular cylinders
en_US
dc.type
Report
ethz.journal.title
SAM Research Report
ethz.journal.volume
2020-14
en_US
ethz.size
56 p.
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09504 - Ammari, Habib / Ammari, Habib
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09504 - Ammari, Habib / Ammari, Habib
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=887
ethz.relation.isPreviousVersionOf
handle/20.500.11850/643004
ethz.date.deposited
2020-08-27T09:45:39Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.identifier.internal
https://math.ethz.ch/sam/research/reports.html?id=887
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-08-27T12:08:41Z
ethz.rosetta.lastUpdated
2020-08-27T12:08:41Z
ethz.rosetta.versionExported
true
ethz.COinS
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