This research, developed at the University of Milan (UNIMI) within the Center for Complexity and Biosystems under the guidance of Prof. Stefano Zapperi, investigates the relationship between auxetic behavior and fracture toughness in disordered mechanical metamaterials. Using computational optimization and experimental validation on additively manufactured samples, the study shows that maximizing auxeticity does not automatically lead to higher energy absorption before failure. Instead, the results reveal a trade-off between these properties, providing new insight into the design of lightweight architected materials. The work was also supported by the ARCHIBIOFOAM project, funded by the European Union under Horizon Europe, highlighting the role of advanced computational design and additive manufacturing in the development of next-generation metamaterials.