Abstract
Universal solutions for fiber-reinforced compressible isotropic elastic materials under large elastic deformations are obtained, by using inverse methods.
The following deformations are investigated: bending, stretching and shearing of a rectangular block; straightening, stretching and shearing of a sector of a circular tube; inflation, eversion, extension, torsion, bending and shearing of a sector of a circular tube; inflation and eversion of a spherical shell.
The significance of the reinforcement and the deformed configuration of the fibers is duscussed.
Zusammenfassung
Unter Benützung inverser Methoden werden universelle Lösungen für faser-vorgespanntes, Kompressibles, isotropes, elastisches Material angegeben.
Die folgenden Deformationen werden untersucht: Biegung, Zug und Schub eines rechteckigen Blockes; Ausgradung, Zug und Schub eines Sektors eines Kreisrohrausschnitts; isotrope Dehnung, Umstülpung, Erweiterung, Tordierung, Biegung und Schub eines Sektors eines Kreisrohres; isotrope Dehnung und Umstülpung einer Kugelschale.
Die Bedeutung der Vorspannung und der verformten Konfiguration der Fasern wird diskutiert.
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References
Beskos, D. E., Int. Jl. Solids Structures (in press).
Ericksen, J. L., Jl. of Math. and Phys. 34 (1955) 126
Chaudhry, H. R. and WaryamSingh, Int. Jl. of Non-linear Mech. 4 (1969) 36
Truesdell, C., and W.Noll, The non-linear field theories of mechanics, in Handbuch der Physik, ed. S. Flügge, vol. III/3. Berlin: Springer-Verlag (1965).
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Beskos, D.E. Universal solutions for fiber-reinforced compressible isotropic elastic materials. J Elasticity 2, 153–168 (1972). https://doi.org/10.1007/BF00125524
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DOI: https://doi.org/10.1007/BF00125524