Abstract
Triply Periodic Minimal Surface (TPMS) structures have gained attention for their exceptional strength-to-weight ratios and tunable mechanical properties, owing to their unique topologies. These attributes make them ideal candidates for structural and multifunctional applications. However, accurately predicting their elastic behavior based on key design parameters—such as relative density, unit cell size, and topology—remains underexplored, limiting their optimized application in lightweight engineering. This study aims to develop predictive relationships for estimating the modulus of elasticity of TPMS-like shell-based structures as a function of their defining parameters including relative density, unit cell size, and topology. We will focus on Primitive (P), Gyroid (G), and a novel composite surface (P–G) derived from a weighted combination of Primitive and Gyroid minimal surfaces. Leveraging the Gibson–Ashby scaling law, power law models are derived to predict the elastic modulus validated through finite element analysis (FEA) under periodic boundary conditions. A 2D graph is constructed for standard TPMS geometries, while a 3D graph is developed for the composite surface to visualize the interplay between mixing factor relative density, and unit cell size. The resulting framework bridges the gap between design and mechanical performance prediction for TPMS-like Shell-based Structures by enabling the selection or estimation of elastic properties based on structural parameters, offering a practical design tool for engineers.