Übersicht
Für das hyperelastische, kompressible, durch eine Familie undehnbarer Fasern verstärkte Verbundmaterial wird die allgemeine finite Stoffgleichung aufgestellt; anschließend werden die Stoffgleichungen nach der Theorie zweiter und erster Ordnung mit Hilfe der Methode der asymptotischen Approximation hergeleitet. Auch die linearisierte Stoffgleichung des durch zwei Familien undehnbarer Fasern verstärkten, kompressiblen Verbundwerkstoffs wird ermittelt, wobei sich für den ebenen Verzerrungszustand die gleichen Beziehungen wie beim inkompressiblen, durch eine Familie undehnbarer Fasern verstärkten Verbundmaterial ergeben.
Summary
The general finite constitutive equation for hyperelastic compressible materials reinforced by one family of inextensible fibres is determined and with the aid of the asymptotic approximation method the second- and first-order constitutive equations are derived. The linearized constitutive equation for a compressible composite reinforced by two families of inextensible fibres is also regarded. For plane strain deformations it is found that these equations are also valid for an incompressible material reinforced by a single family of inextensible fibres.
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Avramidis, I.E. Stoffgleichungen nach der Theorie zweiter und erster Ordnung für hyperelastische faserverstärkte Werkstoffe mit inneren Zwangsbedingungen. Ing. arch 46, 261–269 (1977). https://doi.org/10.1007/BF00536962
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DOI: https://doi.org/10.1007/BF00536962