Variational upper-bound method for analysis of plane strain extrusion tests

Yeon Sheng Yang, Wei Ching Yeh

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, a variational method is employed to determine the upper-bound solution of plane strain extrusion problems. Effect of strain-hardening is taken account for in the theoretical analysis. Specifically, the upper-bound energy equation, expressed in terms of the rigid/plastic boundary function, is established as a functional and it is then optimized by using the technique of variational calculus. Consequently, in addition to the kinematically boundary condition, a set of Natural Boundary Conditions (NBCs) can be mathematically derived and applied to determine the upper-bound solution. The results reveals that these NBCs significantly affect the upper-bound solution in deformation behavior of extruded specimen. Further, by comparing the presented results with those determined without taking account for the NBCs and the two centred-fan slip-line field solution, it is fair to conclude that the current results are in best agreement with the experimental data of most plane strain extrusion tests for 3003-F aluminum alloy, performed in this investigation for the purpose of verification.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of the Chinese Society of Mechanical Engineers, Transactions of the Chinese Institute of Engineers, Series C/Chung-Kuo Chi Hsueh Kung Ch'eng Hsuebo Pao
Issue number1
StatePublished - Feb 1997


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