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Fatigue and Collapse of Cyclically Bent Strip of Amorphous Solid

Fatigue caused by cyclic bending of a piece of material, resulting in its mechanical failure, is a phenomenon that had been studied for ages by engineers and physicists alike. In this Letter we study such fatigue in a strip of athermal amorphous solid. On the basis of atomistic simulations we conclude that the crucial quantity to focus on is the {\em accumulated damage}. Although this quantity exhibits large sample-to-sample fluctuations, its dependence on the loading determines the statistics of the number of cycles to failure. Thus we can provide a scaling theory for the Wöhler plots of mean number of cycles for failure as a function of the loading amplitude.