The Application of an Orthogonal Net of Circles to the Problem of Plane Strain in Plasticity

[+] Author and Article Information
R. E. Llorens

The Pennsylvania State University, King of Prussia Graduate Center, King of Prussia, Pa.

H. A. Koenig

University of Connecticut, Storrs, Conn.

J. Appl. Mech 36(4), 736-742 (Dec 01, 1969) (7 pages) doi:10.1115/1.3564764 History: Received April 08, 1968; Revised February 26, 1969; Online September 14, 2011


A geometric proof of Ringleb’s theorem is indicated. Several geometric considerations as they relate to the application of this theorem to the plane-strain problem of plasticity are derived. Two distinct methods of numerical solution, which are direct outgrowths of this analysis, are thoroughly discussed. The ease of their application and the accuracy of the results are discussed with reference to the standard straight-line approximation. The existence of Hencky’s second theorem for problems of plane strain in plasticity is shown to imply certain features which permit absolute estimates of the accuracy of the results.

Copyright © 1969 by ASME
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