Parameter identification of two-time-scale nonlinear transient models

Background Context Material fatigue is one of the key phenomena whose study is essential to design and develop modern industrial parts: many of the classical methods used in the industry, such as those described in Ref. [1], allow to estimate fatigue life through cumulative formulas. However, these latter do not take into account the history associated with the loading, and tend to give poor results as soon as the loading frequencies are high and the inertia effects should be considered. One particularly difficult case of study corresponds to combined cycle fatigue (CCF), where two different periodic loads (generally, one being ‘slow’, the other ‘fast’) are involved. In the meantime, more and more complex material laws have been proposed to describe cyclic behaviors, and the ideal way to use these models consists in solving them in the time domain. As far as the numerical calculation of a time-dependent model is concerned, the question of the computational cost can be of utmost relevance, especially when the considered model deals with fast phenomena, which require the use of very small time steps, when compared with the length of the time interval of study. In order to drastically reduce the computational cost, a periodic time homogenization method can be used when two well-separated time scales exist, and when the components of the applied loading are periodic with respect to the fast time scale [2]. The resulting homogenized model can then be solved with a drastically reduced computational cost, using time steps related to the slow time scale only, whereas the fast time scale is taken into account in an average way in the homogenization scheme. Abstract The aim of this paper is to study two-time-scale nonlinear transient models and their associated parameter identification. When it is possible to consider two well-separated time scales, and when the fast component of the applied loading is periodic, a periodic time homogenization scheme, similar to what exists in space homogenization, can be used to derive a homogenized model. A parameter identification process for this latter is then proposed, and applied to an academic example, which allows to show the benefits of such a strategy.