Summary
Motions of continuous bodies are analyzed and classified in regard of kinematical aspects with the aid of elementary concepts taken from group and lattice theory. Venn-Euler and Hasse diagrams serve for illustration. The groups of d'Alembert, homogeneous, and circulation-preserving motions cover chains of several subgroups, among which simple shearing and extensional motions are chosen as atoms. It appears that extensional (in contradistinction to shearing) motions can be defined as irrotational homogeneous d'Alembert motions with a distinct demarcation in the group lattice. Kinematical and dynamical discussions aim above all at consequences for extensional viscometry, which will form the main subject of successive contributions.
Zusammenfassung
Bewegungen stetiger Körper werden analysiert und in bezug auf kinematische Gesichtspunkte mit Hilfe elementarer Begriffe, die der Gruppenund Verbandstheorie entnommen sind, klassifiziert. Venn-Euler- und Hasse-Diagramme dienen zur Veranschaulichung. Die Gruppen der d'Alembertschen, der homogenen und der zirkulationserhaltenden Bewegungen umfassen Ketten mehrerer Untergruppen, aus denen die einfache Scher- und die Dehnbewegung als Atome gewählt werden. Es scheint, daß man Dehn- (im Gegensatz zu Scher-)bewegungen als drehungsfreie homogene d'Alembertsche Bewegungen bei deutlicher Abgrenzung im Gruppenverband definieren kann. Eröterungen über die Kinematik und Dynamik zielen vor allem ab auf Folgerungen für die Dehnviskometrie, die das Hauptthema einer Reihe von Beiträgen bilden wird.
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Biermann, M. Foundations of extensional viscometry. Acta Mechanica 11, 283–298 (1971). https://doi.org/10.1007/BF01176562
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DOI: https://doi.org/10.1007/BF01176562