Percolation and Elasticity of Networks [Elektronische Ressource] : From Cellular Structures to Fibre Bundles = Perkolation und Elastizität von Netzwerken / Susan Nachtrab. Betreuer: Klaus Mecke

Percolation and Elasticityof NetworksFrom Cellular Structures to Fibre BundlesPerkolation und Elastizitätvon NetzwerkenVon Zellulären Strukturen zu FaserbündelnDer Naturwissenschaftlichen Fakultätder Friedrich-Alexander-Universität Erlangen-NürnbergzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonSusan Nachtrabaus RudolstadtAls Dissertation genehmigt von der Naturwissen-schaftlichen Fakultät der Universität Erlangen-Nürnberg.Tag der mündlichen Prüfung: 9. Dezember 2011Vorsitzender derPromotionskommission: Prof. Dr. Rainer FinkErstberichterstatter: Prof. Dr. Klaus MeckeZweitberichterstatter: Prof. Dr. Ben FabryAbstractA material’s microstructure is a principal determinant of its effective physical properties.Structure-property relationships that provide a functional form for the dependence ofa physical property (e.g. elasticity) on the microstucture’s morphology are essential forthe physical understanding and also the practical application in material design. Thiswork focuses on materials with spatial mesoscopic network structure. A new model withadjustable network topology is introduced and its percolation properties and effectiveelastic properties are examined.In an initially four-coordinated network, ordered or disordered, each vertex is separatedwith probabilityp to form two two-coordinated vertices, yielding network geometries thatchange continuously from network structures to bundles of unbranched, interwoven fibres.