Summary
The symmetrical expansion of a thick spherical shell whose material is isotropic and exhibits hyperelastic behavior before yielding and during elastic unloading and reloading after yielding is considered. It is assumed that the material is incompressible and the elastic constants and yield stress are such that finite elastic strain occurs before yielding. The method of determining the residual stress distribution which results from unloading from the elastic-plastic state is outlined and results are presented graphically for a special case.
Zusammenfassung
Betrachtet wird die symmetrische Ausdehnung einer dicken Kugelschale aus isotropem Werkstoff mit hyperelastischem Verhalten vor dem Fließen, bei elastischer Entlastung und Wiederbelastung nach dem Fließen. Es wird vorausgesetzt, daß der Werkstoff inkompressibel ist und die Fließgrenze und die elastischen Werkstoffparameter solche Werte haben, daß vor dem Fließen endliche elastische Verzerrungen auftreten. Die Methode zur Ermittlung der Restspannungsverteilung, nach Entlastung aus dem elastisch-plastischen Zustand, wird erläutert und Resultate eines Spezialfalles graphisch dargestellt.
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References
Ward, I. M.: The Mechanical Behavior of Poly(ethylene terephthalate), Cryogenic Properties of Polymers (Serafini, T. F., andJ. L. Koenig, eds.). New York: Dekker. 1968.
Koiter, W. T.: General Theorems for Elastic-Plastic Solids, Progress in Solid Mechanics (Hill, R.,ed.). North Holland. 1960.
Sedov, L. I.: An Introduction to the Mechanics of a Continuous Media. Addison-Wesley. 1965.
Backman, M. E.: Form for the Relation Between Stress and Finite Elastic and Plastic Strains Under Impulsive Loading. J. Appl. Phys.35, (1964).
Lee, E. H.: Elastic-Plastic Deformation at Finite Strains. J. Appl. Mech., Trans.A.S.M.E.E 36, 1 (1969).
Green, A. E., andP. M. Naghdi: A General Theory of an Elastic-Plastic Continuum. Arch. Pat. Mech. Anal.18, 251 (1966).
Green, A. E., andP. M. Naghdi: Some Remarks on Elastic-Plastic Deformation at Finite Strain. Int. J. Engng. Sci.9, 1219 (1971).
Green, A. E., andR. T. Shield: Finite Elastic Deformation of Incompressible Isotropic Bodies. Proc. Roy. Soc. (London)A 202 (1950).
Hill, R.: Mathematical Theory of Plasticity. Oxford University Press. 1950.
Reuss, A.: Berücksichtigung der elastischen Formänderungen in der Plastizitätstheorie. ZAMP10, 266 (1930).
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Hrudey, T.M., Haddow, J.B. Elastic-plastic expansion of a thick spherical shell with finite elastic strain. Acta Mechanica 18, 21–34 (1973). https://doi.org/10.1007/BF01173455
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DOI: https://doi.org/10.1007/BF01173455