The objective of this article is to introduce a new method including model order reduction for the life prediction of structures subjected to cycling damage. Contrary to classical incremental schemes for damage computation, a non-incremental technique, the LATIN method, is used herein as a solution framework. This approach allows to introduce a PGD model reduction technique which leads to a drastic reduction of the computational cost. The proposed framework is exemplified for structures subjected to cyclic loading, where damage is considered to be isotropic and micro-defect closure effects are taken into account. A difficulty herein for the use of the LATIN method comes from the state laws which can not be transformed into linear relations through an internal variable transformation. A specific treatment of this issue is introduced in this work.

One of the challenges of fatigue simulation using continuum damage mechanics framework over the years has been reduction of numerical cost while maintaining acceptable accuracy. The extremely high numerical expense is due to the temporal part of the quantities of interest which must reflect the state of a structure that is subjected to exorbitant number of load cycles. A novel attempt here is to present a non-incremental LATIN-PGD framework incorporating temporal model order reduction. LATIN-PGD method is based on separation of spatial and temporal parts of the mechanical variables, thereby allowing for separate treatment of the temporal problem. The internal variables, especially damage, although extraneous to the variable separation, must also be treated in a tactical way to reduce numerical expense. A temporal multi-scale approach is proposed that is based on the idea that the quantities of interest show a slow evolution along the cycles and a rapid evolution within the cycles. This assumption boils down to a finite element like discretisation of the temporal domain using a set of "nodal cycles" defined on the slow time scale. Within them, the quantities of interest must satisfy the global admissibility conditions and constitutive relations with respect to the fast time scale. Thereafter, information of the "nodal cycles" can be interpolated to simulate the behaviour on the whole temporal domain. This numerical strategy is tested on different academic examples and leads to an extreme reduction in numerical expense.