Symmetry limit theory for work-hardening structures in the shakedown region

The symmetry limit theory extended to general discrete structural systems subjected to quasistatic cyclic loading, which has been established by the authors restricted to perfect plasticity, is further extended to hardening plasticity. Constitutive equations for the variation of a steady state are derived by the formulation essentially different from the previous theory, in which basic relations of the plasticity theory, such as a flow rule, a hardening rule and a consistency condition, are applied to each plastic deformation accumulated during the convergent process to an adjacent steady state. The theory is verified through hysteretic response analysis for 2-D finite element models.