# A Computational Framework for 2D Crack Growth Based on the Adaptive Finite Element Method
## 1 Introduction  
For assessing the behavior of a broad range of engineering and physical concerns, the finite element method (FEM) has undoubtedly been the most popular and successful analytical approach. Studying crack propagation is one of FEM's application areas. As a crack grows, components lose their ability to withstand external loads and eventually fail. A rigorous analysis of their durability and an estimation of operational life are required for the computational design of structural components and materials with embedded cracks. Numerous numerical techniques have proven successful in modeling and simulating engineering issues, such as fracture mechanics, where it can be difficult to find an optimal solution due to the singularity of the stress field near the crack tip. These include the extended finite element method (XFEM) [1; 2; 3; 4], finite element method (FEM) [5; 6; 7; 8], discrete element method (DEM) [9; 10; 11], mesh-free method [12], and boundary element method (BEM) [13]. Numerous software programs, including Ansys [14; 15], ABAQUS [16], NASTRAN, FRANC3D, and COMSOL, which are well-known for being in three dimensions, have been developed with general-purpose finite elements, verified, and implemented for crack propagation simulation. These programs are now available to virtually everyone who requests and pays the required fees for them. Crack propagation may also be simulated using a variety of 2D simulation software, such as NASGRO, AFGROOW, FRANC2D, and FASTRAN. In addition, a significant number of researchers have developed reliable methods for estimating the fatigue crack propagation in 2D linear elastic structures under mixed-mode loading [17; 18; 19; 20]. Crack propagation is often simulated in LEFM by using theequivalent stress intensity factor. The stress intensity factors must be precisely evaluated to anticipate the behavior of crack growth. Numerous handbooks provide analytical SIF solutions for ideal crack configurations and loading conditions that could be used with simple and regular structures [21; 22; 23]. Nevertheless, in many structures, the configuration of fatigue cracks is often intricate and irregular, which results in a variety of distinct ways to fail. As a consequence, analytical solutions will not be able to accurately anticipate SIF solutions for these fatigue cracks, which can be estimated using the findings of the FEM. The displacement extrapolation technique [24; 25] and the J-integral method [26; 27; 28] are the two approaches used most often to calculate SIFs. The trajectory of a crack's propagation may be predicted using a variety of approaches including the theory of maximum circumferential stress, the theory of maximum energy release, and the theory of minimum strain-energy density. In this work, an automated adaptive mesh finite element is used to simulate mixed-mode crack propagation in the presence of holes using developed source code written in the Visual Fortran language. The outcomes acquired using the developed program are similar to those obtained using commercial fracture mechanics software, e.g., [29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. In regard to knowledge, utilizing source code is appropriate for at least two purposes: first, understanding the basic algorithm that it uses, and second, acquiring programming expertise in its development. This study also shows a scientific methodology that researchers may follow as a guideline to build their own programs at the lowest possible cost when compared to commercial software.