Summary
The mechanical response predicted by the constitutive equation of a non-simple elastic material is considered in relation to the total strain behaviour of an elastic-plastic solid extensively deformed in the range of plastic strain. Both loading and unloading are considered in relation to the range of total elastic-plastic strain. In the absence of appropriate experimental studies, comparison of the predictions of the proposed constitutive equation of a non-simple elastic material, when applied to the work-hardening behaviour of the material, has been restricted to a study of the characteristic stress-strain behaviour of a strain hardening material. This has centred on the correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple compression, simple torsion and pure shear with the object of obtaining a universal stress-strain curve.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Billington, E. W.: Constitutive equation for a class of non-simple elastic materials. Acta Mech.62, 143–154 (1986).
Lode, W.: Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel. Z. Phys.36, 913–939 (1926).
Lee, E. H.: Elastic-plastic deformation at finite strains. J. Appl. Mech.36, 1–6 (1969)
Freund, L. B.: Constitutive equations for elastic-plastic materials at finite strain. Int. J. Solids Struct.6, 1193–1209 (1970).
Hahn, H. T., Jaunzemis, W.: A dislocation theory of plasticity. Int. J. Engng. Sci.11, 1065–1078 (1973).
Hahn, H. T.: A finite-deformation theory of plasticity. Int. J. Solids Struct.10, 111–121 (1974).
Lee, E. H., Germain, P.: Elastic-plastic theory at finite strain, in: Sawczuk, A., ed.: Intn. Symposium on Foundations of Plasticity: II Problems of Plasticity, pp. 117–133, Leyden: Noordhoff 1974.
Billington, E. W.: Generalised isotropic yield criterion for incompressible materials. Acta Mech.72, 1–20 (1988).
Ludwik, P.: Elemente der Technologischen Mechanik. Berlin: Springer-Verlag 1909.
Ludwik, P., Scheu, A.: Vergleichende Zug-, Druck-, Dreh- und Walzversuche. Stahl u. Eisen45, 373–381 (1925).
Billington, E. W.: The Poynting-Swift effect in relation to initial and post-yield deformation. Int. J. Solids Struct.21, 355–371 (1985).
Billington, E. W.: Non-linear mechanical response of various metals: I. Dynamic and static response to simple compression, tension and torsion in the as-received and annealed states. J. Phys. D10, 519–531 (1977).
Lianis, G., Ford, H.: An experimental investigation of the yield criterion and the stress-strain law. J. Mech. Phys. Solids5, 215–222 (1957).
Taylor, G. I., Quinney, H.: The plastic distortion of metals. Phil. Trans. R. Soc. Lond.A 230, 323–362 (1931).
Author information
Authors and Affiliations
Additional information
With 1 Figure
Rights and permissions
About this article
Cite this article
Billington, E.W. Constitutive equation of a non-simple elastic plastic material. Acta Mechanica 72, 21–37 (1988). https://doi.org/10.1007/BF01176541
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01176541