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Numerical simulations have the potential to be used for designing damage-tolerance composite structures. However, numerical models are currently computationally intensive, and their post-failure evolution and fracture morphology predictions are still limited. In the present work, a numerical methodology to simulate advanced composite joints is presented. The results of a numerical campaign aimed to evaluate the progressive damage and failure analysis (PDFA) of an advanced pin-hole connection under tensile and compressive load are evaluated. A high-fidelity stacked shell-cohesive methodology is employed to simulate the ultimate load, fracture initiation, and propagation of the proposed composite joint. Post-failure erosion methodology is proposed to control the initiation and evolution of composite fractures. The location and extension of the numerically predicted damages are compared with experimental observations. The proposed methodology demonstrates its preliminary ability to be used for designing composite joints up to failure. Specific outcomes are also pointed out.