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research-article

On Prager's hardening rule

Published: 01 September 1958 Publication History

Zusammenfassung

Um das Verhalten eines Metalls mit dem Spannungs-Dehnungs-Diagramm der Figur 1 unter einem beliebigen räumlichen Spannungszustand zu beschreiben, wird neben der Annahme isotroper Verfestigung, welche aber den Bauschinger-Effekt nicht erklärt, die Pragersche Verfestigungsregel [8] verwendent. Es wird hier untersucht, welche Formen diese Regel in den wichtigsten Spannungsräumen von weniger als neun Dimensionen annimmt.

References

[1]
H. Ziegler,An Attempt to Generalize Onsager's Principle, and Its Significance for Rheological Problems, Z. angew. Math. Phys.9b, 748 (1958).
[2]
R. v. Mises,Mechanik der festen Körper im plastisch deformablen Zustand, Göttinger Nachrichten, Math. phys. Kl.1913, 582 (1913).
[3]
H. Tresca Mémoire sur l'écoulement des corps solides, Mém. prés. Acad. Sci., Paris18, 733 (1868).
[4]
R. v. Mises,Mechanik der plastischen Formänderung von Kristallen, Z. angew. Math. Mech.8, 161 (1928).
[5]
D. C. Drucker,Some Implications of Work Hardening and Ideal Plasticity, Quart. appl. Math.7, 411 (1950).
[6]
R. Hill,The Mathematical Theory of Plasticity (Oxford 1950).
[7]
P. G. Hodge, Jr.,The Theory of Piecewise Linear Isotropic Plasticity, IUTAM Colloquium Madrid 1955,Deformation and Flow of Solids (Berlin 1956).
[8]
W. Prager,The Theory of Plasticity: A Survey of Recent Achievements (James Clayton Lecture), Proc. Inst. Mech. Eng.169, 41 (1955).
[9]
W. Prager,Probleme der Plastizitätstheorie (Basel 1955), p. 16.
[10]
P. G. Hodge, Jr.,Piecewise Linear Plasticity, Proc. 9th Intern. Congr. Appl. Mech., Brussels, 1956.

Cited By

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  • (2023)A Novel Implicit Stress Integration Algorithm and its Verification Using von Mises and Drucker Prager PlasticityProceedings of the 2023 15th International Conference on Computer Modeling and Simulation10.1145/3608251.3608283(63-71)Online publication date: 16-Jun-2023

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    Published In

    cover image Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
    Zeitschrift für Angewandte Mathematik und Physik (ZAMP)  Volume 9, Issue 3
    Sep 1958
    105 pages

    Publisher

    Birkhauser Verlag

    Switzerland

    Publication History

    Published: 01 September 1958

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    1. Mathematical Method

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    • (2023)A Novel Implicit Stress Integration Algorithm and its Verification Using von Mises and Drucker Prager PlasticityProceedings of the 2023 15th International Conference on Computer Modeling and Simulation10.1145/3608251.3608283(63-71)Online publication date: 16-Jun-2023

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