Thin‐layer inertial effects in plasticity and dynamics in the Prandtl problem

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dc.contributor.authorGeorgievskii, Dmitri V.
dc.contributor.authorMüller, Wolfgang H.
dc.contributor.authorAbali, Bilen Emek
dc.date.accessioned2020-02-13T14:53:15Z
dc.date.available2020-02-13T14:53:15Z
dc.date.issued2019-10-23
dc.description.abstractEspecially in metal forming, large plastic deformation occurs in thin plates. The problem of compressing dies is analyzed to evaluate the spreading of a thin layer in between. The velocity of dies is a given function in time so that the kinematics of the process is known. This problem can be considered as a generalization of the classical Prandtl problem by taking inertial effects into account and introducing dimensionless parameters as internal variables depending on time. The first parameter is purely geometric corresponding to the thin‐layer approximation; the second and the third parameters are dimensionless velocity and acceleration during the dies getting pressed. We use singular asymptotic expansions of unknown functions and study how these parameters vary preceding the dies of moment. Depending on this relation, the dynamic corrections to the quasistatic solution is a part of various terms of the asymptotic series. The corresponding analytical investigation both for general case and for particular typical regimes of plates motion is carried out.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel - 2019en
dc.identifier.eissn1521-4001
dc.identifier.issn0044-2267
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/10761
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-9656
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 Mathematiken
dc.subject.ddc530 Physiken
dc.subject.otheranalytical mechanicsen
dc.subject.otherinertial effectsen
dc.subject.otherplasticityen
dc.subject.otherthin layersen
dc.titleThin‐layer inertial effects in plasticity and dynamics in the Prandtl problemen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumbere201900184
dcterms.bibliographicCitation.doi10.1002/zamm.201900184
dcterms.bibliographicCitation.issue12
dcterms.bibliographicCitation.journaltitleZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechaniken
dcterms.bibliographicCitation.originalpublishernameWileyen
dcterms.bibliographicCitation.originalpublisherplaceBerlinen
dcterms.bibliographicCitation.volume99
tub.accessrights.dnbfree
tub.affiliationFak. 5 Verkehrs- und Maschinensysteme::Inst. Mechanik::FG Kontinuumsmechanik und Materialtheoriede
tub.affiliation.facultyFak. 5 Verkehrs- und Maschinensystemede
tub.affiliation.groupFG Kontinuumsmechanik und Materialtheoriede
tub.affiliation.instituteInst. Mechanikde
tub.publisher.universityorinstitutionTechnische Universität Berlinde

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