Luigi Greco

Graduation: Civil Engineering at University of Pavia

Supervisor: Prof. Alessandro Reali, Prof. Matteo Negri, Dr. Alessia Patton

Thesis title: Isogeometric methods for the study of fracture mechanics via phase-field modelling

Abstract: The thesis investigates phase-field models for brittle fracture, with a focus on higher-order formulations. It begins by comparing second-order and fourth-order AT2 models, showing that higher-order approaches can achieve similar accuracy while allowing for coarser meshes, thus improving computational efficiency. To better evaluate crack evolution, an image-based skeletonization algorithm is also introduced. Building on these results, a novel fourth-order AT1 model is proposed, combining the favorable physical properties of AT1 (such as a clear elastic limit and sharper crack transitions) with the numerical advantages of higher-order regularization. The model is supported by a theoretical analysis based on Γ-convergence, which provides key parameters such as the corrected toughness and transition width. Numerical results demonstrate improved accuracy compared to existing models. Finally, the study is extended to dynamic fracture, analyzing the influence of different time-integration schemes and phase-field formulations on wave propagation and computational cost. In this context, higher-order models show even greater advantages, particularly in reducing the number of required time steps.