Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.
A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 12, 2002; final revision, Jan. 10, 2003. Associate Editor: M.-J. Pindera. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Zhang, Y., Hao, H., and Yu, M. (October 10, 2003). "A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems ." ASME. J. Appl. Mech. September 2003; 70(5): 649–654. https://doi.org/10.1115/1.1602484
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