Summary
In isotropic, incompressible simple materials there are five known families of dynamically possible inhomogeneous finite deformations. It is shown that these deformations are also possible in isotropic, elastic-inelastic materials with temperature independent response. The method of solution is an inverse one. The deformation is specified precisely at the outset, and the problem of finding the surface tractions which are required in order to maintain the deformation is reduced to the problem of solving a system of ordinary differential equations.
Zusammenfassung
In isotropen inkompressiblen einfachen Substanzen mit Gedächtnis gibt es fünf Gruppen von dynamisch möglichen nicht-homogenen Deformationen. In der Arbeit wird gezeigt, dass diese Gruppen von Deformationen auch in isotropen inkompressiblen elastisch-inelastischen Substanzen dynamisch möglich sind. Die vorgeschlagene Methode stellt einen inversen Lösungstyp dar. Die Deformationen werden als gegebene Funktionen der Zeit vorausgesetzt, und das Problem der Berechnung der Oberflächenspannungen, welche diese Deformationen erzeugen, wird auf die Lösung eines Systems von gewöhnlichen Differentialgleichungen reduziert. Es wird auch gezeigt, dass die Anzahl der Gleichungen in diesem System für keine der erwähnten Gruppen von Deformationen 3+n übersteigt, wobein die Zahl der Strukturparameter ist, die die elastisch-inelastische Substanz charakterisieren.
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Kratochvíl, J. Dynamically possible finite deformations of isotropic, incompressible, elastic-inelastic solids with temperature independent response. Journal of Applied Mathematics and Physics (ZAMP) 23, 949–959 (1972). https://doi.org/10.1007/BF01596222
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DOI: https://doi.org/10.1007/BF01596222