  For the numerical simulation of time-dependent problems, recent works suggest
the use of a time marching scheme based on a tensorial decomposition of the
time axis. This time-separated representation is straightforwardly introduced
in the framework of the Proper Generalized Decomposition (PGD). The time
coordinate is transformed into a multi-dimensional time through new separated
coordinates, the micro and the macro times. From a physical viewpoint, the time
evolution of all the quantities involved in the problem can be followed along
two time scales, the fast one (micro-scale) and the slow one (macro-scale). In
this paper, the method is applied to compute the quasi-static response of an
elasto-plastic structure under cyclic loadings. The study shows the existence
of a physically consistent temporal decomposition in computational cyclic
plasticity. Such micro-macro characterization may be particularly appealing in
high-cycle loading analyses, such as aging and fatigue, addressed in a future
work in progress.
