Function-based parametric design of additively manufactured graded cellular structures for mechanical and thermal performance

Graded cellular structures have attracted increasing attention for lightweight and multifunctional applications. However, most existing gradation definitions are qualitative, limiting systematic exploration of their potential in multifunctional design. This study proposes a function-based parametric strategy to tailor the mechanical and thermal performance of two-dimensional (2D) graded cellular structures. By parameterizing key geometric features of regularly patterned structures with mathematical functions, both the dimensionless elastic modulus (E*) and the dimensionless thermal conductivity (K*) can be effectively tuned at a fixed overall infill porosity (P). Comparative analyses highlight the critical roles of porosity and the gradation function form. At P = 40%, quadratic gradations expand the tunable performance range by up to 50% relative to linear gradations. Furthermore, quadratic-graded structures achieve up to 2.1-fold wider tunability in E* and 3.7-fold in K* compared with randomly patterned counterparts, which exhibit narrower, near-normal performance distributions. To address trade-offs in multifunctional design, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to optimize the gradation coefficients. The resulting Pareto fronts show an approximately linear trade-off between E* and K* under the same gradation strategy, revealing promising sub-regions for high-stiffness, low-thermal-conductivity designs. Overall, this work offers a computationally light, physically interpretable approach for the multifunctional design of graded cellular structures, with strong potential for applications in thermal protection, energy absorption, and architected metamaterials.