Vol 57, No 2-3 (2005)

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Direct methods for limits in plasticity

A.R.S. Ponter, H.F. Chen

Arch. Mech. 57 (2-3), 171-187, 2005



The paper discusses a methodology for the evaluation of shakedown and ratchet limits for an elastic perfectly plastic solid subjected to mechanical and thermal cycles of loading. The steady cyclic state is characterised by a minimum theorem that contains the classical shakedown theorems as a special case. For a prescribed class of kinematically admissible strain rate histories, the minimum of the functional is found by a programming method, the Linear Matching Method, which converges to the least upper bound. Three examples are given for a finite element implementation, rolling contact on a half-space, the behaviour of a complex heat exchanger and the behaviour of a regular particulate metal matrix composite subjected to variable temperature.

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