Evolution of surfaces and the kinematics of membranes

Kadianakis, N

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	https://dspace.lib.ntua.gr/xmlui/handle/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