Time-independent constitutive theories for cyclic plasticity

The article is mainly concerned with time-independent plasticity in the range of cyclic loadings. Three different approaches are considered for the description of kinematic behaviour: (i) the use of independent multiyield surfaces, (ii) models with two surfaces only, (iii) the so-called “nonlinear-kinematic hardening rule” defined by a differential equation. The thermodynamic framework from which the third approach is derived and the conditions of varying temperature are considered. Connections between the three kinds of models are pointed out. Also, some specific rules to describe cyclic hardening or cyclic softening of the material are proposed. Finally, the limits of the models considered, and the difficulties associated with their practical use and their implementation in computer codes are discussed in detail.