I am trying to extrapolate damage in cyclic fatigue tests ( and if possible creep-fatigue tests as well). Without damage I have used the method by Bogard et al. (https://asmedigitalcollection.asme.org/materialstechnology/article/132/2/021003/461079/Damage-and-Rupture-Simulation-for-Mechanical-Parts) which has been not bad. I have a damage rate equation which does not follow classical Hayhurst formulation. I was wondering whether anyone has tried efficient cycle jump algorithms with fatigue. A general direction towards such studies would be helpful as well.