Summary
TheColeman-Noll approach to the thermodynamics of materials is applied to the case of plasticity. The essential constitutive property is that the dependent thermodynamic variables are functions of the deviators of both the stress and strain, but are otherwise independent of time in the same sense as elastic substances. The conclusion is then deduced, from the second law, that for such materials the loading and unloading stress-strain relations must be different; thus the essential feature of plasticity is deduced in a rational way. The second law is also shown to imply a material stability which is formally of theDrucker type.
Zusammenfassung
Die Festkörper-Thermodynamik in der Fassung vonColeman undNoll wird auf den Fall der Plastizität angewendet. Die wesentliche Materialeigenschaft ist, daß die abhängigen thermodynamischen Variablen einerseits Funktionen sowohl des Spannungs- als auch des Verzerrungsdeviators sind, andererseits aber in gleicher Weise wie bei elastischen Stoffen unabhängig von der Zeit angenommen werden. Für die so definierten Materialien folgt aus dem zweiten Hauptsatz ein wesentliches Merkmal der Plastizität: die Verschiedenheit von Belastungs- und Entlastungslinie. Ferner wird gezeigt, daß der zweite Hauptsatz eine Material-Stabilitätsaussage beinhaltet, die formal derDruckerschen entspricht.
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Dillon, O.W. A thermodynamic basis of plasticity. Acta Mechanica 3, 182–195 (1967). https://doi.org/10.1007/BF01453714
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DOI: https://doi.org/10.1007/BF01453714