## 2 The Present Issue  
This Special Issue attempted to gather the latest research on the numerical approaches for the simulation of fracture problems, a very hot topic in research at the present time [1; 2; 3]. Particularly, this SI focused on simulations for both traditional (e.g., metal materials) and innovative materials (e.g., composites or additively manufactured) through the usage of different numerical approaches. When possible, the papers highlighted not only the enhanced accuracy but also the computational time efficiency. The propagation of cracks and defects in structures depends on the cyclic loads applied on it, such as mechanical, thermal, residual stresses, etc. This highlights the need to account for all kinds of loading conditions in simulating the fracture problem. In [4], for the first time, Adapcrack3D has been adopted to simulate three-dimensional problems by considering cyclic mechanical loads and static thermal loads. Adapcrack3D was updated to work with FE models comprising multiple parts and relevant features such as coupling and surface interactions. Additionally, Adapcrack3D used the submodel technique for the fracture mechanics assessments, comprising the architecture of the submodel modified to simulate models with contacts defined between the crack faces. The software was tested with different 3D models and the results were in a good agreement with the experimental and numerical reference data. The results confirmed that the simulation of contacts in Adapcrack3D was a major step in improving the functionality of the program. Various practical application areas were also highlighted, in which this newly implemented feature in Adapcrack3D can be applied, e.g., fatigue crack growth in gears, bearings, rolling contact fatigue in rails, etc. When referring to the propagation of cracks in vessels and pipelines, leaks and ruptures may result in substantial environmental consequences and income losses for the oil and gas industry. To reduce the failure probability and at the same time to retain the system's design capacity, the technical conditions of pipelines have to be periodically controlled by in-line inspections, which are scheduled in order to detect potential damages or defects that can endanger the system's loading capacity. In [5], a numerical-experimental study has been performed for a composite-repaired pipeline made of API 5L X60 steel. An experimental burst test was carried out on a 4 m long pipe section and tested up to the complete failure. The test was simulated numerically by means of an FEM model of the composite-repaired steel tank in such a way to allow for a cross-comparison of the outcomes. It was found that the investigated composite repairing technique eliminated almost the whole noteworthy thickness reduction of nearly 80% and the related stress concentrations in the pipe. Similarly to oil and gas, the aircraft industry has required in recent decades the accurate prediction of the propagation of cracks. As a matter of fact, traditional crack initiation criteria have been lately replaced by damage tolerance concepts, as pushed by the challenging requirements related to weight and, consequently, to fuel consumption. This applies for instance to blisks (blades and disk), in which a crack, triggered by vibrations at the blade root, may (depending on the propagation direction) grow through the disk and lead to the complete catastrophic failure due to centrifugal loading. In [6], the focus was on the calculation of the propagation direction by using two kink angle calculation criteria, i.e., the averaged angle criterion and the dominant step criterion. The prediction results were compared with the experimental data obtained with tension-torsion tests with and without considering a phase shift between the loads. It was found that the dominant step criterion demonstrated slightly better results for small to moderate values of the phase shift, whereas not very consistent results and no decisive conclusions were drawn for cases with a large phase shift of nearly 90\({}^{\circ}\).