Summary
This paper studies the mechanism of shock formation from generalised simple waves in the case of an isotropic incompressible hyperelastic material. Fast and slow waves are identified and it is established that slow simple waves cannot tend to shocks on the wavefront. The time and position of occurrence of shocks when they do form is investigated with the aid of generalised Riemann invariants and a circularly polarised slow wave is identified. The special case of plane shear waves is commented upon.
Zusammenfassung
Diese Arbeit beschäftigt sich mit dem Mechanismus der Ausbildung von Stoßfronten aus verallgemeinerten einfachen Wellen im Fall eines isotropen inkompressiblen hyperelastischen Werkstoffes. Schnelle und langsame Wellen werden identifiziert und es wird festgestellt, daß langsame einfache Wellen nicht zur Ausbildung von Stoßfronten an der Wellenfront führen können. Zeit und Ort des Auftretens von Stoßfronten, sofern sie sich bilden, werden mit Hilfe von verallgemeinerten Riemannschen Invarianten untersucht und eine zirkular-polarisierte langsame Welle wird identifiziert. Der Spezialfall ebener Scherwellen wird diskutiert.
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Jeffrey, A., Teymur, M. Formation of shock waves in hyperelastic solids. Acta Mechanica 20, 133–149 (1974). https://doi.org/10.1007/BF01374966
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DOI: https://doi.org/10.1007/BF01374966