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The Quarterly Journal of Mechanics and Applied Mathematics 1989 42(1):13-21; doi:10.1093/qjmam/42.1.13
© 1989 by Oxford University Press
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NECESSARY AND SUFFICIENT CONDITIONS FOR THE VALIDITY OF A WORK INEQUALITY IN FINITE PLASTICITY

H.-C. LIN and P. M. NAGHDI

( Department of Mechanical Engineering, University of California Berkeley, California 94720, USA )

A physically plausible work assumption, stated in the form of an integral inequality over an arbitrary cycle of homogeneous motion, was introduced in (1); and several conditions, necessary for the validity of this work inequality, have been derived in recent years for finitely deforming elastic-plastic materials. The main purpose of the present paper is to identify the conditions which are also sufficient for the validity of the work inequality. The proof of sufficiency suggests alternative and more direct derivations for two of the necessary conditions. An outline of the proofs of these is also indicated.


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