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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):18-28; doi:10.1093/qjmam/1.1.18
© 1948 by Oxford University Press
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A VARIATIONAL PRINCIPLE OF MAXIMUM PLASTIC WORK IN CLASSICAL PLASTICITY

R. HILL

( Cavendish Laboratory Cambridge )

The classical equations of Lévy-Mises and Prandtl-Reuss for an ideally plastic material are reviewed. A variational principle of maximum plastic work is derived for plastic states of stress satisfying the Lévy-Mises relation and the Huber-Mises yield criterion. Uniqueness theorems are established for a completely plastic body under prescribed boundary conditions. The variational principle is applied to the problem of a uniform bar of arbitrary section deformed in combined tension, torsion, and bending


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