Design methodology of functionally graded cellular materials: Manipulating design parameters of triply periodic minimal surfaces through three-dimensional density distributions

Functionally Graded Cellular Materials (FGCM) with variable volume fractions have demonstrated significant advantages, including weight reduction, improved stiffness, and enhanced load distribution, when compared to uniform density counterparts. Their design is often characterized by the application of a density distribution to locally modify Representative Volume Elements (RVEs). Current studies have explored the application of Triply Periodic Minimal Surfaces (TPMS) topologies, given their capability to create seamless and interconnected structures, thus avoiding stress concentration issues commonly encountered in traditional lattice configurations. Consequently, this paper introduces a design methodology tailored to TPMS-based FGCM allowing for independent or simultaneous adjustments of RVE thickness and size. Models for predicting relative density as a function of the RVE design parameters of Primitive and Gyroid topologies are presented and discussed. These models are employed to adapt the topologies to three-dimensional density distributions. The proposed method is implemented as a set of design tools and is illustrated for the studied TPMS topologies.