A constitutive model for elastoplastic deformation under variable amplitude multiaxial cyclic loading

This paper discusses the applicability of recently reported plastic flow equations (based on the concept of distance in the stress space) to variable amplitude multiaxial cyclic loading. The main aim of these equations is to provide the means to generalize to the multiaxial case some of the techniques commonly employed nowadays by fatigue designers which are known collectively as the Local Strain Approach to (low cycle) fatigue. The stress space is assumed to have a non-Euclidean metric where hydrostatic directions are null displacements of zero length. The structure of the metric is reflected in the form of the yield surfaces of the material and it can thus be inferred from the yield criterion. Consideration of unloading processes leads to the analysis of equivalent paths and to the definition of a generalized separation, which provides a new representation of kinematic hardening. The generalization of the well known memory effect to the multiaxial case arises naturally from the formalism presented.