Symmetry limit theory for elastic-perfectly plastic continua in the shakedown region

The symmetry limit theory, originally developed for beam-columns with uni-axial constitutive relations, is extended to elastic-perfectly plastic continua in the shakedown region. In the symmetry limit theory, we trace the steady-state path, or the variation of a steady-state cyclic response under an idealized cyclic loading program with continuously increasing amplitude. A steady-state response is represented by a set of the equilibrium configurations at load reversals. Key extension in the present theory is the derivation of the multi-axial constitutive relations for tracing the steady-state path. Noting that plastic strains are constant throughout a steady cycle in shakedown elements, we derive tbe constitutive relations in which stress rates and strain rates at load reversals may be coupled. With these constitutive relations, the symmetry limit can be found as the first branching point of the steady-state path. The present theory is verified through numerical examples. (C) 2000 Published by Elsevier Science Ltd.