Summary
In previous work the authors have shown examples of the concept of ideal viscoplasticity applied to the analysis of rate sensitive material response. The aim of these idealizations has been to generate reasonably simple solutions that exhibit the essential features found experimentally. In this paper a closed form solution is developed for the problem of a shock wave propagating without change of shape. A very simple approximate expression is found that is in excellent agreement with the exact solution, and simple approximations are obtained for the largest strain rate and the shock thickness. The solution implies that dislocation behavior rather than non-linearity in the material pressure, volume relation is primarily responsible for the decrease of shock thickness with impact intensity.
Zusammenfassung
In einer vorangegangenen Arbeit haben die Autoren Beispiele der Anwendung der idealen Viskoplastizität zur Untersuchung des Verhaltens geschwindigkeitsabhängiger Werkstoffe gezeigt. Ziel dieser Idealisierungen war die Entwicklung einfacher Lösungen, die jedoch die wesentlichen, experimentell gefundenen Erscheinungen wiedergeben. In dieser Arbeit wird eine geschlossene Lösung des Problems der Ausbreitung einer Stoßwelle ohne Gestaltswechsel entwicklet. Ein sehr einfacher Näherungsausdruck, der ausgezeichnet mit der exakten Lösung übereinstimmt, wird gefunden, und einfache Näherungen für die größte Verzerrungsgeschwindigkeit und die Stoßwellendicke werden angegeben. Die Lösung zeigt, daß vor allem Versetzungsverhalten und weniger die Nichtlinearität im Druck-Volumen-Gesetz für den Abfall der Stoßwellendicke mit zunehmender Stoßintensität verantwortlich ist.
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Kelly, J.M., Gillis, P.P. An ideally viscoplastic analysis of shock profiles. Acta Mechanica 26, 47–57 (1977). https://doi.org/10.1007/BF01177135
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DOI: https://doi.org/10.1007/BF01177135