Elastic and failure properties of 2D primitive TPMS lattices with varying shape factor

Abstract

Architected materials based on Triply Periodic Minimal Surfaces (TPMS) have demonstrated outstanding mechanical performance; however, their two-dimensional (2D) counterparts remain insufficiently explored. This study presents a comprehensive numerical investigation of the elastic response and failure behavior of 2D Primitive TPMS lattice structures, with particular emphasis on the role of geometric parameters C₁ and C₂. A phase-field damage framework is employed to capture the full mechanical evolution, from initial elastic deformation to crack initiation and subsequent propagation leading to ultimate failure. The results reveal that mechanical performance is governed not only by relative density but also critically by geometric configuration. In particular, structures with nearly identical relative densities can exhibit strength variations of up to five times, underscoring the dominant influence of shape parameters. In addition, certain configurations display pronounced auxetic behavior, with a minimum Poisson’s ratio of −0.12 observed for C₁ = 1.2 and C₂ = 0.8. Failure consistently initiates at the specimen center, where stress concentration is most severe. Overall, this study provides both a high-quality numerical dataset and fundamental insights into the geometry–mechanical performance relationship of 2D TPMS lattices. The findings establish a foundation for the rational design and optimization of TPMS-based architected materials in advanced engineering applications.