New formulation of nonlinear kinematic hardening model, Part I: A Dirac delta function approach

A new mathematical modelling framework for simulation of metal cyclic plasticity is proposed and experimental validation based on tension-compression cyclic testing of S355J2 low carbon structural steel presented over the two parts of this paper. The advantages and limitations of the stress-strain curve shape modelling given by "Armstrong and Frederick" type hardening rules are discussed and a new formulation for kinematic hardening is proposed for more accurate representation of the stress-strain dependence under cyclic loading conditions. The proposed model is shown to describe the shape of the stress-strain curve accurately under various different loading conditions. Transition effects occurring at loading reversals are incorporated through a new framework of Dirac delta functions. In addition to the yield surface, stress supersurfaces able to expand and instantly move to simulate a shift of stress-strain curves during loading reversals are determined. This also enables inclusion of the behaviour of monotonic stress-strain curves with yield plateau deformation in one mathematical model. The influence of the first stress invariant on the shape of a stress-strain curve in tension and compression directions observed in many metals is incorporated into the kinematic hardening rule. The ability of the model to accurately describe transition from elastic to elastic-plastic deformation at small offset strain yield points naturally accounts for nonlinearity of an unloading stress-strain curve after plastic pre-strain. Development of the model to include mixed cyclic hardening/softening, ratcheting and mean stress relaxation is presented in a companion paper (Part II), which includes experimental validation of the modelling framework.