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Strut-based cellular structures have gained remarkable attention in recent years due to their improved strength-to-weight ratio, energy absorption abilities, and heat transfer properties. A key feature of cellular structures employed in modern infrastructure and devices is a symmetric configuration with repeating unit cells. This periodic design makes fabrication more feasible for next-generation aerospace and biomedical materials. However, such a design with brittle constituents often undergoes a sudden and catastrophic failure as all unit cells along a fracture surface tend to fail simultaneously at a critical loading condition. In this paper, we propose an elegant solution to achieve progressive failure by adjusting the diameter of each strut to create asymmetric or irregular cellular structures. Finite element simulations are conducted and validated by comparing with experiments on additively manufactured samples. Designs are then categorized into three failure modes and the relationship between the failure modes and the stress–strain curves are analyzed. Lastly, simulation-based Bayesian optimization is applied to design the structures with a more distributed stress field before failure and therefore improve their strength and energy absorption capabilities. Results show that the proposed designs fail at the boundaries and the cracks grow locally without penetrating through the entire structure, leading to more progressive failure. This research proposes novel cellular structures via symmetry breaking to achieve structures with promising manufacturability and damage-tolerant failure, greatly broadening their applications.