Summary
This paper is concerned with the finite spherically symmetric motion of a compressible hyperelastic spherical shell, subjected to a spatially uniform step funtion application of pressure at its inner surface. A method, given in a previous paper [1], for the determination of the field of characteristics, for expansion of a spherical cavity in an unbounded solid is adapted to consider the spherical shell problem. Results are presented graphically for a particular strain energy function and are compared with results obtained for an incompressible material and from linear elasticity theory.
Zusammenfassung
Diese Arbeit befaßt sich mit der endlichen, kugelförmig-symmetrischen Bewegung einer kompressiblen hyperelastischen Kugelschale, die auf der Innenseite durch eine räumlich gleichförmige Druck-Sprungfunktion belastet wird. Eine Methode, wie sie in einer früheren Arbeit [1] zur Bestimmung des Charakteristikenfeldes für die Aufweitung eines kugelförmigen Hohlraumes in einem unendlich ausgedehnten Festkörper gegeben ist, wird für die Behandlung des Kugelschalenproblems erweitert. Die Resultate werden graphisch für eine besondere Verzerrungsenergiefunktion angegeben und mit Resultaten für inkompressibles Material und Resultaten der linearen Elastizitätstheorie verglichen.
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Haddow, J.B., Mioduchowski, A. Dynamic expansion of a compressible hyperelastic spherical shell. Acta Mechanica 26, 179–187 (1977). https://doi.org/10.1007/BF01177145
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DOI: https://doi.org/10.1007/BF01177145