Evolution of surfaces and the kinematics of membranes

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dc.contributor.author Kadianakis, N en
dc.date.accessioned 2014-03-01T01:33:27Z
dc.date.available 2014-03-01T01:33:27Z
dc.date.issued 2010 en
dc.identifier.issn 0374-3535 en
dc.identifier.uri http://hdl.handle.net/123456789/20426
dc.subject Kinematics en
dc.subject Membranes en
dc.subject Surfaces en
dc.subject.classification Engineering, Multidisciplinary en
dc.subject.classification Materials Science, Multidisciplinary en
dc.subject.classification Mechanics en
dc.subject.other Field theory en
dc.subject.other Gauss curvature en
dc.subject.other Geometrical quantities en
dc.subject.other Moving surfaces en
dc.subject.other Non-linear en
dc.subject.other Polar decompositions en
dc.subject.other San Diego en
dc.subject.other Second fundamental form en
dc.subject.other Shape operators en
dc.subject.other Continuum mechanics en
dc.subject.other Domain decomposition methods en
dc.subject.other Elasticity en
dc.subject.other Kinematics en
dc.subject.other Mathematical operators en
dc.subject.other Theorem proving en
dc.subject.other Three dimensional en
dc.subject.other Two dimensional en
dc.subject.other Membranes en
dc.title Evolution of surfaces and the kinematics of membranes en
heal.type journalArticle en
heal.identifier.primary 10.1007/s10659-009-9226-0 en
heal.identifier.secondary http://dx.doi.org/10.1007/s10659-009-9226-0 en
heal.language English en
heal.publicationDate 2010 en
heal.abstract The polar decomposition theorem for a two dimensional continuum (a membrane) is used to produce a set of equations that describe the evolution of the geometrical quantities of a moving surface, i.e., the metric, the unit normal, the shape operator, the second fundamental form, the mean and the Gauss curvature. A link to the kinematical quantities of the continuum is also given. The version of the polar decomposition theorem for membranes we use was proved by Chi-Sing Man and H. Cohen (J. Elast. 16:97-104, 1986). Both the geometric and the kinematical framework are coordinate-free, in an attempt to contribute to a coordinate-free description for the kinematics of membranes in analogy to the kinematics of three dimensional continuum bodies as it emerges from the classical works of Noll (Arch. Rat. Mech. Anal. 2:197-226, 1958), Truesdell and Noll (The Non-linear Field Theories of Mechanics, 3rd edn., Springer, Berlin, 2004), Truesdell (A First Course in Rational Continuum Mechanics, vol. 1, Academic Press, San Diego, 1977). © 2009 Springer Science+Business Media B.V. en
heal.publisher SPRINGER en
heal.journalName Journal of Elasticity en
dc.identifier.doi 10.1007/s10659-009-9226-0 en
dc.identifier.isi ISI:000274251600001 en
dc.identifier.volume 99 en
dc.identifier.issue 1 en
dc.identifier.spage 1 en
dc.identifier.epage 17 en

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