Numerical Modeling and Optimization of Fractured Structures via Machine Learning and Topology Optimization

Abstract

During the continuous development of science and technol- ogy, optimization plays a tremendous role in improving our resources without compromising the quality of performance. This thesis work investigates the application of the phase- field method for fracture (PFF) in brittle materials, focusing on the understanding of the influence of the model parame- ters, both for the isotropic and the anisotropic cases, in cap- turing the mechanical response of experimental results. For the PFF isotropic case, an experimental investigation was car- ried out on an ABS co-polymers. A MATLAB-based algo- rithm combining particle swarm optimization (PSO) with PFF has been utilized to determine optimal values of Young’s mod- ulus (E), fracture toughness (Gc), and the PFF internal length scale (lc) through uni-axial tensile and three-point bending tests. To understand the potential of bio-polymers in vari- ous industrial applications, 3D printed PLA materials were fabricated via fusion deposition modeling, and due to their anisotropic behavior, an anisotropic PFF approach was ex- ploited. A metaheuristic machine learning algorithm coupled with PFF demonstrates robustness in estimating fracture pa- rameters (Gc, lc, β) and a strong influence of β the penalty parameter on the predicted force-displacement curves. The thesis examine also the critical issue of delamination at internal interfaces/adhesive joints and internal cracks in com- posite and multi-material components, which can lead to catas- trophic failures. Existing structural topology optimization (TO) methods typically assumes perfect bonding, which urges the development of approaches that explicitly optimize struc-tures against delamination. The proposed data-driven heuris- tic optimization strategy has been applied to identify optimal cohesive interface properties with linear grading, enhancing the composite structure’s resistance to peeling. Additionally, it explored the application of the Solid Isotropic Material with Penalty (SIMP) topology optimization approach to optimize substrate internal structures affected by interface delamina- tion. The integration of a phase-field for fracture (PFF) approach with TO has been highlighted as a robust mathematical frame- work to mitigate crack progression in structures compromised by initial damage under operational loads. Employing the SIMP technique and optimality criteria (OC) method, the re- search validated its effectiveness through numerical exam- ples, demonstrating potential improvements in fracture re- sistance for damaged structures crucial in aerospace, marine, automotive, and civil engineering industries