Constitutive equation of a non-simple elastic plastic material. (English) Zbl 0635.73042
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 absense 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 centered 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.
MSC:
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74A20 | Theory of constitutive functions in solid mechanics |
| 74B99 | Elastic materials |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
Keywords:
work-hardening; non-simple elastic material; total strain behaviour; elastic-plastic solid extensively deformed; plastic strain; loading; unloading; total elastic-plastic strain; characteristic stress-strain behaviour; strain-hardeningReferences:
| [1] | Billington, E. W.: Constitutive equation for a class of non-simple elastic materials. Acta Mech.62, 143-154 (1986). · Zbl 0607.73002 · doi:10.1007/BF01175860 |
| [2] | Lode, W.: Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel. Z. Phys.36, 913-939 (1926). · doi:10.1007/BF01400222 |
| [3] | Lee, E. H.: Elastic-plastic deformation at finite strains. J. Appl. Mech.36, 1-6 (1969) · Zbl 0179.55603 |
| [4] | Freund, L. B.: Constitutive equations for elastic-plastic materials at finite strain. Int. J. Solids Struct.6, 1193-1209 (1970). · Zbl 0211.28404 · doi:10.1016/0020-7683(70)90056-9 |
| [5] | Hahn, H. T., Jaunzemis, W.: A dislocation theory of plasticity. Int. J. Engng. Sci.11, 1065-1078 (1973). · Zbl 0272.73052 · doi:10.1016/0020-7225(73)90109-2 |
| [6] | Hahn, H. T.: A finite-deformation theory of plasticity. Int. J. Solids Struct.10, 111-121 (1974). · Zbl 0272.73027 · doi:10.1016/0020-7683(74)90104-8 |
| [7] | 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. |
| [8] | Billington, E. W.: Generalised isotropic yield criterion for incompressible materials. Acta Mech.72, 1-20 (1988). · Zbl 0635.73041 · doi:10.1007/BF01176540 |
| [9] | Ludwik, P.: Elemente der Technologischen Mechanik. Berlin: Springer-Verlag 1909. · JFM 40.0753.05 |
| [10] | Ludwik, P., Scheu, A.: Vergleichende Zug-, Druck-, Dreh- und Walzversuche. Stahl u. Eisen45, 373-381 (1925). |
| [11] | Billington, E. W.: The Poynting-Swift effect in relation to initial and post-yield deformation. Int. J. Solids Struct.21, 355-371 (1985). · Zbl 0564.73053 · doi:10.1016/0020-7683(85)90061-7 |
| [12] | 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). · doi:10.1088/0022-3727/10/4/016 |
| [13] | Lianis, G., Ford, H.: An experimental investigation of the yield criterion and the stress-strain law. J. Mech. Phys. Solids5, 215-222 (1957). · doi:10.1016/0022-5096(57)90007-8 |
| [14] | Taylor, G. I., Quinney, H.: The plastic distortion of metals. Phil. Trans. R. Soc. Lond.A 230, 323-362 (1931). · Zbl 0003.08003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
