A mathematical analysis of the elasto-plastic anti-plane shear problem of a power-law material and one class of closed-form solutions

International Journal of Solids and Structures

Volumn 33, Issue 15, 1996, Pages 2213-2223

  Gao, Xin Lin ^a,b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; ELASTOPLASTICITY; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SHEAR STRESS;

DIFFERENTIAL TRANSFORMATION; ELASTOPLASTIC ANTIPLANE SHEAR PROBLEM; HENCKY'S DEFORMATION THEORY; INFINITESIMAL DEFORMATION; VON MISES' YIELD CRITERION;

STRUCTURAL ANALYSIS;

EID: 0030174151     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7683(95)00049-6     Document Type: Article

References (23)

1. Abeyaratne, R. and Horgan, C. O. (1983). Bounds on stress concentration factors in finite antiplane shear. J. Elasticity 13, 49-61.
2. Adkins, J. E. (1954). Some generalizations of the shear problem for isotropic incompressible materials. Proc. Cambr. Phil. Soc. 50, 334-345.
3. Amazigo, J. C. (1974). Fully plastic crack in an infinite body under anti-plane shear. Int. J. Solids Structures 10, 1003-1015.
4. Atkin, R. J. and Fox, N. (1980). An Introduction to the Theory of Elasticity, pp. 157-158. Longman, London.
5. Boresi, A. P. and Chong, K. P. (1987). Elasticity in Engineering Mechanics, pp. 28-29. Elsevier, New York.
6. Eshelby, J. D. (1979). Boundary problems. In Dislocations in Solids : The Elastic Theory (Edited by F. R. N. Nabarro), Vol. 1, pp. 167-222. North-Holland, Amsterdam.
7. Flanigan, F. J. (1972). Complex Variables, Harmonic and Analytic Functions, pp. 148-193. Allyn and Bacon, Boston.
8. Gurtin, M. E. and Temam, R. (1981). On the anti-plane shear problem in finite elasticity. J. Elasticity 11, 197-206.
9. Horgan, C. O. and Miller, K. L. (1994). Antiplane shear deformations for homogeneous and inhomogeneous anisotropic linearly elastic solids. ASME J. Appl. Mech. 61, 23-29.
10. Ilyushin, A. A. (1946). The theory of small elastic-plastic deformations. Prikl. Mat. Mekh. 10, 347-356.
11. Jiang, Q. and Knowles, J. K. (1991). A class of compressible elastic materials capable of sustaining finite anti-plane shear. J. Elasticity 25, 193-201.
12. Knowles, J. K. (1976). On finite anti-plane shear for incompressible elastic materials. J. Aust. Math. Soc. Ser. B 19, 400-415.
13. Knowles, J. K. (1977a). A note on anti-plane shear for compressible materials in finite elastostatics. J. Aust. Math. Soc. Ser. B 20, 1-7.
14. Knowles, J. K. (1977b). The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Int. J. Fracture 13, 611-639.
15. Koskinen, M. F. (1963). Elastic-plastic deformation of a single grooved flat plate under longitudinal shear. ASME J. Bas. Engng 85, 585-594.
16. Milne-Thomson, L. M. (1962). Antiplane Elastic Systems. Springer, Berlin.
17. Muskhelishvili, N. I. (1953). Some Basic Problems of the Mathematical Theory of Elasticity, pp. 129-134. P. Noordhoff, Groningen, Holland.
18. Neuber, H. (1961). Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. ASME J. Appl. Mech. 28, 544-550.
19. Polignone, D. A. and Horgan, C. O. (1992). Axisymmetric finite anti-plane shear of compressible nonlinearly elastic circular tubes. Q. Appl. Math. 50, 323-341.
20. Raymond, J.-P. (1993). An anti-plane shear problem. J. Elasticity 33, 213-231.
21. Rice, J. R. (1966). Contained plastic deformation near cracks and notches under longitudinal shear. Int. J. Fracture Mech. 2, 426-447.
22. Rice, J. R. (1967). Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear. ASME J. Appl. Mech. 34, 287-298.
23. Tuba, I. S. (1969). A perturbation theory of antiplane elastic-plastic deformations. Int. J. Non-Linear Mech. 4, 51-60.