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Abstract:
Simple theories of plasticity such as flow rules associated with a single yield surface are sufficiently accurate in predicting plastic behaviour for monotonic loading. However, for alternating or cyclic loads, such theories cannot describe complex plastic behaviour with sufficient accuracy. The concept of multiple loading surfaces or internal state parameters may then be introduced and respective plasticity theories become considerably complicated, requiring step by step integration of incremental relations for both strain and internal parameters.

The present paper is aimed at elaborating relatively simple models of cyclic behaviour that could be expressed in terms of generalized stresses and strains and could be applied in treating boundary-value problems for beams, plates and shells. Finite stress-strain relations are derived in several subdomains of the stress space, both for loading, unloading and subsequent loading conditions. It is assumed that a set of discrete points from the past history affects the actual state. Some particular cases of cyclic loading of a tube and circular plates are considered in detail in order to illustrate applicability of proposed description.