PSI - Issue 81

Ivan Pidgurskyi et al. / Procedia Structural Integrity 81 (2026) 47–53

49

Fig. 2. Main algorithm for determining the stress intensity factor (SIF) for surface cracks using the finite element method.

The issue of generating a high-quality yet computationally efficient mesh within the indicated algorithm is crucial for solving solid mechanics problems involving cracks. The quality of the computational mesh affects the convergence of the solution process, while its efficiency determines the time required for the analysis. The generally accepted FEM procedure for solving fracture mechanics problems for bodies with surface cracks involves the generation of three types of meshes (Pidgurskyi et al., 2022): an initial (global) mesh for the entire body, a local mesh containing the surface crack that is integrated into the body, and a finite element mesh in the transition zone (Fig. 3). When addressing FEM problems for determining the SIF along the front of coplanar surface cracks, the finite element mesh is generated in a manner similar to that used for a single crack; however, a number of additional conditions must be satisfied. At the initial stage, curvilinear “tubes” surrounding the front of each crack are created and discretized into finite elements in th e circumferential and radial directions (Fig. 3).

Fig. 3. Finite element mesh modeling in a plate with two coplanar surface cracks: (a) general view; (b) features of merging the local finite element mesh with the transition-zone mesh.

Thus, for a reliable assessment of the influence of adjacent cracks on variations in the SIF along their fronts, the cracks should be positioned as close to each other as possible. The maximum allowable proximity of cracks can be established during finite element mesh generation, provided that the following conditions are satisfied (Duarte, 2015; Pidgurskyi, 2018; Pidgurskyi et al., 2022): (a) prevention of overlap of the projections of the tubes, since such overlap makes finite element mesh generation impossible;