The computational model is combined with Enhanced Assumed Strain (EAS) and Assumed Natural Strains (ANS) to alleviate locking pathology concerning the solid shell formulation, leading to a coupled non-linear variational formulation. The three-dimensional Kirchhoff-Saint-Venant constitutive model is modified to accommodate the functional grading of the material properties. The formulation of the current model is constructed via the evaluation of the phase-field in the Clausius-Duhem inequality leading to first-order stability conditions in order to ensure thermodynamic consistency. Based on this practical relevance, a thermodynamically consistent framework is proposed in this investigation for solving the coupled thermo-mechanical phase-field fracture problem in thin-walled structures made of FGMs. Thermo-elastic fracture is a matter of important concern for thin-walled structures made of functionally graded materials (FGMs). These are important properties that must be treated accurately in order to yield an accurate model for arbitrary load sequences, where various amplitude loading occurs. We show that the model developed within this study is able to predict realistic fatigue crack growth behavior in terms of accurate growth rates and also to account for mean stress effects and different stress ratios. Furthermore, the level of the mean load has a significant effect. Besides the pure magnitude of a certain load cycle, it is highly decisive at which point of the fatigue life a certain load cycle is applied. The load time function applied to a certain structure has an essential effect on its fatigue life. With other words, the crack surface energy is not solely in competition with the time-dependent elastic strain energy but also with a contribution consisting of accumulated energies, which enables crack extension even for small maximum loads. For crack growth due to cyclic fatigue, our basic approach considers an additional energy contribution entering the regularized energy density function accounting for crack driving forces associated with fatigue damage. So far, phase field fracture models were applied to a number of problems in the field of fracture mechanics and were proven to yield reliable results even for complex crack problems. Within this work, we utilize the framework of phase field modeling for fracture in order to handle a very crucial issue in terms of designing technical structures, namely the phenomenon of fatigue crack growth.
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