PSI - Issue 66

5

Domenico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 396–405 Author name / Structural Integrity Procedia 00 (2025) 000–000

400

Essentially, the adaptive mesh technique is based on three key elements:

(i) Discretize the entire structure into a grid of macro-elements. (ii) Remove the macro-elements within a zone of interest, which must contain the expected location of damage nucleation (light blue zone in initial stage of Fig. 2). (iii) Choose a proper insert criterion, which defines when and where fine meshes should be introduced. The criterion just mentioned, based on damage crack phase-field variable ( c  ) at micro-macro interfaces, is the following:   c c toll.    (7) It is important to note that, the adaptive mesh strategy, by focusing mesh refinement only in the zone of interest, not only improves the accuracy of the solution but also significantly enhances the overall computational efficiency. 3.2. Adaptive cohesive phase-field crack propagation algorithm The adaptive cohesive phase-field crack propagation process employed in this study is numerically implemented via a user-made script written in Java language, developed using the Model Builder application, which is integrated within the adopted commercial finite element software COMSOL Multiphysics (COMSOL, 2024). The following outlines the main steps of the developed automatic algorithm. The script code begins by defining the geometry, mechanical properties and boundary conditions. After that, the computational domain is divided into macro-subdomains, whereas within a zone of interest, micro-subdomains are inserted. In particular, the macro subdomains are meshed with a single finite element, while the micro-subdomains are discretized using a fine mesh. Continuity conditions, through the collocation method, are imposed at the interface between the macro and micro subdomains to ensure that transition between two different meshes does not introduce artificial discontinuities in the displacement fields and/or stress distributions. At this point, the numerical simulation starts by increasing the control displacement. For each increment, the code checks the damage conditions at micro-macro interfaces via Eq. (7). The interface where the damage crack phase field variable is greater than a set threshold is designated as a critical micro-macro interface, and the adjacent macro subdomain is marked as critical macro-element. As soon as a critical macro-element is found, it is deactivated, and the damaging fine mesh is inserted in this region. This refinement allows an accurate resolution of crack propagation in the cracked region without the need to refine the mesh across the entire computational domain. Finally, the algorithm checks if the structure reaches the collapse. If the total failure occurs, the simulation stops. If not, the process continues by refining more regions as damage progresses.