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The classical theory of univalent functions and quasistatic crack propagation

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dc.contributor.authorOleaga Apadula, Gerardo Enrique
dc.date.accessioned2023-06-20T09:28:27Z
dc.date.available2023-06-20T09:28:27Z
dc.date.issued2006
dc.description.abstractWe study the propagation of a crack in critical equilibrium for a brittle material in a Mode III field. The energy variations for small virtual extensions of the crack are handled in a novel way: the amount of energy released is written as a functional over a family of univalent functions on the upper half plane. Classical techniques developed in connection to the Bieberbach Conjecture are used to quantify the energy-shape relationship. By means of a special family of trial paths generated by the so-called Löwner equation we impose a stability condition on the field which derives in a local crack propagation criterion. We called this the anti-symmetry principle, being closely related to the well known symmetry principle for the in-plane fields.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/12568
dc.identifier.doi10.1017/S0956792506006577
dc.identifier.issn0956-7925
dc.identifier.officialurlhttp://journals.cambridge.org/action/displayJournal?jid=EJM
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49652
dc.issue.number02
dc.journal.titleEuropean Journal of Applied Mathematics
dc.language.isoeng
dc.page.final255
dc.page.initial233
dc.publisherCambridge University Press
dc.relation.projectIDBFM 2004-05634
dc.relation.projectIDSFB 611
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.keywordCrack propagation
dc.subject.keywordMode III
dc.subject.keywordUnivalent functions
dc.subject.keywordLoewner equation
dc.subject.keywordSchifferd´s method
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleThe classical theory of univalent functions and quasistatic crack propagation
dc.typejournal article
dc.volume.number17
dspace.entity.typePublication
relation.isAuthorOfPublication8a7b6bff-4e63-42ed-bb95-31a089c7d57f
relation.isAuthorOfPublication.latestForDiscovery8a7b6bff-4e63-42ed-bb95-31a089c7d57f
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