Thermomechanical performance of double-phase periodic and graded architected materials: Numerical and explainability analysis

Abstract

The work investigates the effective thermomechanical performance of double-phase architected materials as a function of their inner design. The effective thermal conductivity, Young’s and shear moduli of double-phase composites, engineered with a wide range of Gielis’-formula-based topological architectures are analyzed, deriving analytical expressions for their effective performance. Thereupon, the effect of the addition of a second thermally isolating or conductive and mechanically soft or stiff phase is quantified for different phase combinations, including metal–metal, metal–ceramic or metal–epoxy designs, material pairs encountered in engineering practice. Moreover, the impact of material grading is assessed, establishing and quantifying differences among the effective mechanical and thermal attributes. It is shown that the Young’s modulus is mainly controlled by the shape of the second phase, while the effective thermal conductivity arises as a combination of the underlying pattern and phase properties. High-fidelity neural network (NN) models are developed and used as a basis for interpretability, SHapley Additive exPlanations (SHAP) analysis. Highly nonlinear dependencies on the inner design features are reported, with feature interactions well-beyond the bounds of single-phase material designs. The role of shape effects is quantified as more prominent for comparatively low conductivity and soft second phase designs. In such a space, the Young’s $\hat{E}$ and shear $\hat{G}$ modulus are 33% and 100% more sensitive to the inner structural pattern than the effective thermal conductivity $\hat{k}$. The relative significance of topology is substantially mitigated for composites with comparable phase conductivities and stiffness ratios, with importance values that are nearly seven times lower than the ones computed for the second phase volumetric content.