A variational framework for the efficient simulation of fatigue

High computational requirements often limit the feasibility of fatigue simulations for complex structures or predictions over long lifetimes. This paper introduces an innovative and efficient methodology for modeling fatigue without the excessive processing times typically required for cycle-by-cycle simulations. By introducing a coordinate transformation from the parameter of time to the cycle number, a significant reduction in computational costs is achieved. Furthermore, this strategy enables the efficient construction of force-displacement hysteresis loops and facilitates the investigation of low-cycle fatigue, high-cycle fatigue, and the endurance limit. The model is based on an extended Hamilton principle of stationary action and is implemented using the Neighbored Element Method. The properties of this strategy are demonstrated through various boundary value problems, demonstrating its robustness and effectiveness.