A kinetic two-scale damage model for high-cycle fatigue simulation using multi-temporal Latin framework

The goal of this paper is to introduce a model order reduction method for high-cycle fatigue simulations using a kinetic damage model, i.e. a constitutive model in which the damage evolution law is defined as a rate form D ˙ = d d t D for the damage variable D. In the framework of continuum mechanics, high-cycle fatigue simulation involves a two-scale damage model, which includes macroscopic elastic and microscopic plastic behaviours, for a very large number of cycles. Unlike the classical usage of the two-scale damage model by Lemaitre and co-workers, where damage is calculated as a post-process of an elastic or elasto-plastic macroscopic analysis, in this work, a fully coupled analysis is conducted assuming a macroscopic damage feedback from its microscopic counterpart. Damage is considered to be isotropic with micro-defect closure effect on both macroscopic and microscopic scales. To overcome the numerical expense, the large time increment (LATIN) method is used as a linearisation framework, where the constitutive behaviour is separated from the global admissibility which in turn is solved through separation of variables using a proper generalised decomposition (PGD)-based model reduction method. A multi-temporal discretisation approach is henceforth used based on finite element like description in time for the quantities of interest, providing a sophisticated numerical approach suitable for high-cycle fatigue simulation under complex loading.