A phase-field fracture model for fatigue using locking-free solid shell finite elements: Analysis for homogeneous materials and layered composites

A computational framework to model fatigue fracture in structures based on the phase-field method and the solid-shell concept is herein presented. With the aim of achieving a locking free solid-shell finite element formulation with fracture-prediction capabilities, both the combination of the Enhanced Assumed Strain (EAS) and Assumed Natural Strain (ANS) methods with phase field of fracture is exploited. In order to achieve realistic prediction, the crack driving force is computed using positive/negative split of the stress field. Moreover, the difference between the driving forces are pinpointed. Furthermore, based on thermodynamic considerations, the free energy function is modified to introduce the fatigue effect via a degradation of the material fracture toughness. This approach retrieves the SN curves and the crack growth curve as expected. The predictive capability of the model is evaluated through benchmark examples that include a plate with a notch, a curved shell, mode II shear, and three-point bending for homogeneous materials, as well as a dogbone specimen for homogenized fiber-reinforced composites. Additionally, comparative analysis is performed with previous results for the plate with notch and mode II shear tests, while the dogbone specimen is compared with experimental data to further validate the accuracy of the present model.