A mathematical analysis of the elasto-plastic plane stress problem of a power-law material

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 60, Issue 2, 1998, Pages 139-149

  Gao, Xin Lin ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; DEFORMATION; ELASTOPLASTICITY; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; STRAIN; STRESS ANALYSIS;

ELASTOPLASTIC PLANE STRESS PROBLEMS; POWER LAW MATERIALS;

NUMERICAL ANALYSIS;

EID: 0032040788     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/60.2.139     Document Type: Article

References (21)

1. CAPSONI, A. & CORRADI, L. 1996 Variational formulations for the plane strain elastic-plastic problem for materials governed by the von Mises criterion. Int. J. Plasticity 12, 547-560.
2. CHOU, P. C. & PAGANO, N. J. 1967 Elasticity: Tensor, Dyadic, and Engineering Approaches. Princeton: Van Nostrand.
3. ENGLAND, A. H. 1971 Complex Variable Methods in Elasticity. London: Wiley.
4. GAO, XIN-LIN 1994 Finite deformation elasto-plastic solution for the pure bending problem of a wide plate of elastic linear-hardening material. Int. J. Solids Structures 31, 1357-1376.
5. GAO, XIN-LIN 1996a A general solution of an infinite elastic plate with an elliptic hole under biaxial loading. Int. J. Pres. Ves. Piping 67, 95-104.
6. GAO, XIN-LIN 1996b A mathematical analysis of the elasto-plastic anti-plane shear problem of a power-law material and one class of closed-form solutions. Int. J. Solids Structures 33, 2213-2223.
7. GAO, Y.-C. & HWANG, K.-C. 1983 On the formulation of plane strain problems for elastic perfectly-plastic medium. Int. J. Engng Sci. 21, 765-780.
8. GU, QIU-LIN 1982 A general asymptotic analytical solution of plane problem of elasto-plasticity with strain hardening. Acta Mech. Sinica 25, 82-89.
9. HILL, R. 1950 The Mathematical Theory of Plasticity. Oxford: University Press.
10. MORGAN, C. O. 1995 Anti-plane shear deformations in linear and nonlinear solid mechanics. SIAM Review 37, 53-81.
11. HUANG, Y. M. 1989 Determination of individual stresses from thermoelastically measured trace of stress tensor. Ph.D. dissertation, University of Wisconsin-Madison, Madison, Wisconsin, USA.
12. HUANG, Y. M. & ROWLANDS, R. E. 1991 Quantitative stress analysis based on the measured trace of the stress tensor. J. Strain Anal. 26, 55-63.
13. HUTCHINSON, J. W. 1968 Singular behaviour at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16, 13-31.
14. LEE, Y. S. & SMITH, L. C. 1988 Analysis of a power-law material containing a single hole subjected to a uniaxial tensile stress using the complex pseudo-stress function. ASME J. Appl. Mech. 55, 267-274.
15. MUSKHELISHVILI, N. I. 1953 Some Basic Problems of the Mathematical Theory of Elasticity. Groningen: Noordhoff.
16. PENG, YAFEI, SHEN, YAPENG & CHEN, YIHENG 1996 Some faults in the stress analysis of power-hardening materials with pseudo-stress function method. ASME J. Appl. Mech. 63, 554-555.
17. PRAGER, W. & HODGE, P. G. 1951 Theory of Perfectly Plastic Solids. New York: Wiley.
18. RICE, J. R. & ROSENGREN, G. F. 1968 Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16, 1-12.
19. TEODORESCU, P. P. 1966 One hundred years of investigations in the plane problem of the theory of elasticity. In Applied Mechanics Surveys (ed. H. N. Abramson, H. Liebowitz, J. M. Crowley and S. Juhasz). Washington: Spartan Books, 245-262.
20. WANG, ZI-KUNG, WEI, XUE-XIA & GAO, XIN-LIN 1991 Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function.
21. WESTERGAARD, H. M. 1952 Theory of Elasticity and Plasticity. Cambridge (Ma.): Harvard University Press.