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TECHNICAL PAPERS

A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

[+] Author and Article Information
Y.-Q. Zhang

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore

H. Hao

Department of Civil and Resource Engineering, University of Western Australia, Crawley, Western Australia 6009

M.-H. Yu

School of Civil Engineering and Mechanics, Xi’an Jiaotong University, Xi’an 710049, Xi’an, China

J. Appl. Mech 70(5), 649-654 (Oct 10, 2003) (6 pages) doi:10.1115/1.1602484 History: Received July 12, 2002; Revised January 10, 2003; Online October 10, 2003
Copyright © 2003 by ASME
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References

Johnson, W., Sowerby, R., and Venter, R. D., 1982, Plane Strain Slip Line Fields for Metal Deformation Processes—A Source Book and Bibliography, Pergamon Press, Oxford.
Lee,  Y. K., 1989, “Conditions for Shear Banding and Material Instability in Finite Elastoplastic Deformation,” Int. J. Plast., 5, pp. 197–226.
Runesson,  K., Ottosen,  N., and Peric,  D., 1991, “Discontinuous Bifurcations of Elastic-Plastic Solutions at Plane Stress and Plane Strain,” Int. J. Plast., 7, pp. 99–121.
Collins,  I. F., and Dewhurst,  P., 1993, “A Matrix Technique for Constructing Slip-Line Field Solutions to a Class of Plane-Strain Plasticity Problems,” Int. J. Numer. Methods Eng., 7, pp. 357–378.
Panayotounakos,  D., 1996, “Ad Hoc Exact Solutions for the Stress and Velocity Fields in Rigid Perfectly Plastic Materials Under Plane-Strain Conditions,” Int. J. Plast., 12, pp. 1069–1190.
Panayotounakos,  D., 1999, “Ad Hoc Exact Solutions for the Stress and Velocity Fields in Rigid Perfectly Plastic Materials Under Plane-Stress Conditions,” Int. J. Non-Linear Mech., 34, pp. 71–84.
Kachanov, L. M., 1971, Foundations of the Theory of Plasticity, North-Holland Publication Co., Amsterdam.
Yan, Z., 1988, Theory of Plasticity, Tianjin University Publishing House, Tianjin (in Chinese).
Lubliner, J., 1990, Plasticity Theory, Macmillan Publishing Company, New York.
Yan, Z., and Bu, X., 1992, “The Method of Characteristics for Solving the Plane Stress Problem of Ideal Rigid-Plastic Body on the Basis of Twin Shear Stress Yield Criterion,” Proc. of the Asia-Pacific Symposium on Advances in Engineering Plasticity and Its Application, Elsevier, Hong Kong.
Yan,  Z., and Bu,  X., 1996, “An Effective Characteristic Method for Plastic Plane Stress Problems,” J. Eng. Mech., 122, pp. 502–506.
Yu,  M., 1983, “Twin Shear Stress Yield Criterion,” Int. J. Mech. Sci., 25, pp. 71–74.
Yu,  M., 2002, “Advance in Strength Theory of Material and Complex Stress State in the 20th Century,” Appl. Mech. Rev., 55, pp. 169–218.
Fan,  S. C., Yu,  M. H., and Yang,  S. Y., 2001, “On the Unification of Yield Criteria,” J. Appl. Mech., 68, pp. 341–343.
Yu,  M., He,  L., and Song,  L., 1985, “Twin Shear Strength Theory and its Generalization,” Sci. Sin., Ser. A, 28, pp. 1174–1183.
Yu, M., and He, L., 1991, “A New Model and Theory on Yield and Failure of Materials Under Complex Stress State,” Mechanical Behavior of Materials ∼6, Pergamon Press, New York, 3 , pp. 841–846.
Shield,  R. T., 1954, “Stress and Velocity Fields in Soil Mechanics,” J. Math. Phys., 33, pp. 144–156.
Chen, W. F., 1975, Limit Analysis and Soil Plasticity, Elsevier, Amsterdam.

Figures

Grahic Jump Location
Different yield loci on the π plane for non-SD materials (α=1)
Grahic Jump Location
Different yield loci on the π plane for SD materials (0<α<1)
Grahic Jump Location
An infinite thin plate with a circular hole under a two-directional uniform tension at infinity
Grahic Jump Location
Characteristics and stress distribution
Grahic Jump Location
Acute wedge under unilateral pressure
Grahic Jump Location
The relation between the limit load pu and the parameter b

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