Summary
Rate equations for internal variables are not invariant under transformations to other sets of internal variables if such transformations involve the external variables (deformation, temperature), unless the rate equations include the rates of the external variables as well. The simplest invariant rate equations are linear in the external-variable rates; for materials with such rate equations, thermodynamic relations are studied, and conditions are obtained for the reducibility of such rate equations to a form without external-variable rates. Materials with plastic behavior have rate equations that are piecewise linear in the external-variable rates, and thermodynamic relations for such materials are studied as well.
Zusammenfassung
Geschwindigkeitsgleichungen der inneren Zustandsvariablen sind nicht invariant gegen Transformation auf andere innere Zustandsvariable, wenn diese Transformation äußere Zustandsvariable (Deformation, Temperatur) einschließt, außer die Geschwindigkeitsgleichungen enthalten auch Ableitungen äußerer Zustandsvariablen nach der Zeit. Die einfachsten invarianten Geschwindigkeitsgleichungen sind linear in den Ableitungen der äußeren Zustandsvariablen. Für durch solche Gleichungen beschreibbare Werkstoffe werden thermodynamische Beziehungen untersucht und Bedingungen für die Reduzierbarkeit dieser Geschwindigkeitsgleichungen auf Formen, die keine Ableitungen äußerer Zustandsvariablen enthalten, abgeleitet. Werkstoffe mit plastischem Verhalten besitzen Geschwindigkeitsgleichungen, die abschnittsweise linear in den Ableitungen der äußeren Zustandsvariablen sind. Thermodynamische Beziehungen solcher Stoffe werden ebenfalls untersucht.
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Lubliner, J. On the structure of the rate equations of materials with internal variables. Acta Mechanica 17, 109–119 (1973). https://doi.org/10.1007/BF01260883
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DOI: https://doi.org/10.1007/BF01260883