Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-20T06:49:35.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Basic stress analysis of hyperbolic regimes in plastic media

Published online by Cambridge University Press:  24 October 2008

R. Hill
R. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear problems of two-dimensional deformation or stress in solid continua are considered where the in-plane components of stress are self-equilibrated and subject to a scalar constraint. In applications the latter is often a yield condition for plastic media. Such field equations are frequently hyperbolic, with a pair of characteristic curves through any point. The primary aim is to express the integrable differential relations along the curves in their simplest form, by an optimal choice of coordinates and variables. Special cases of this problem are now classical, but the general case has received little attention and the universal canonic structure of the relations has escaped notice.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 359 - 369
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Booker, J. R. and Davis, E. H.A general treatment of plastic anisotropy under conditions of plane strain. J. Mech. Phys. Solids 20 (1972), 239–250.CrossRefGoogle Scholar
(2)Hencky, H.Über einige statisch bestimmte Fälle des Gleichgewichte im plastischen Körper. Z. angew. Math. Mech. 3 (1923), 241–251.CrossRefGoogle Scholar
(3)Hill, R.The theory of plane plastic strain for anisotropic metals. Proc. Roy. Soc. London A 198 (1949), 428–437.Google Scholar
(4)Hill, R.The Mathematical Theory of Plasticity, (Oxford: Clarendon Press, 1950).Google Scholar
(5)Hill, R.The extrernal stress-field concept. J. Mech. Phys. Solids 14 (1966), 239–243.CrossRefGoogle Scholar
(6)Hill, R.Theoretical plasticity of textured aggregates. Math. Proc. Cambridge Philos. Soc. 85 (1979), 179–191.CrossRefGoogle Scholar
(7)Hill, R.On the theory of plane strain in finitely deformed compressible materials. Math. Proc. Cambridge Philos. Soc. 86 (1979), 161–178.CrossRefGoogle Scholar
(8)Kötter, F.Die Bestimmung des Druckes an gekrümmten Gleitflächen, eine Aufgabe aus der Lehre vom Erddruck. Ber. Akad. Wiss., Berlin (1903), 229–233.Google Scholar
(9)Mandel, J. Equilibres par tranches planes des solides. Proc. 6th Int. Cong. Appl. Mech., Paris, (1946).Google Scholar
(10)Rice, J. R.Plane-strain slip-line theory for anisotropic rigid/plastic materials. J. Mech. Phys. Solids 21 (1973), 63–74.CrossRefGoogle Scholar
(11)Sokolovsky, V. V.Theory of plasticity, (Moscow, 1946).Google Scholar