Development of a thermomechanical model for fracture under monotonic and cyclic loading with enhanced strain accuracy

Fatigue is a critical issue in many engineering applications, particularly in components subjected to cyclic loading. The complexity of fatigue is further exacerbated by thermal effects, which significantly influence material degradation and failure mechanisms. Addressing the challenge of accurately simulating high cycle fatigue failure under thermomechanical conditions is essential for improving the reliability and safety of structures in thermally aggressive environments. In this work, we present a staggered thermomechanical approach, grounded in enhanced accuracy mixed finite elements, coupled with a high cycle fatigue constitutive law. This model is generalized to incorporate thermal effects, enabling a more reliable prediction of fatigue damage in materials subjected to cyclic thermal and mechanical loads. The staggered strategy efficiently decouples the thermal and mechanical fields, improving computational performance without compromising accuracy. Furthermore, we make use of an advanced time-stepping strategy, which significantly reduces the overall computational cost by optimizing the progression of the simulation through cycles, especially in regimes where fatigue evolves slowly. This approach allows for a more efficient analysis of long-term fatigue behaviour under varying thermal conditions. The proposed method has been validated through multiple examples, demonstrating its effectiveness and precision in predicting fatigue life and crack propagation in thermomechanical environments.