Effective thermal conductivity prediction and thermomechanical cross-property relation of spinodal metamaterials

Controlling thermal conductivity is essential for manipulating heat flux, a task that often requires metamaterials with highly anisotropic and spatially non-uniform properties. This study investigates the thermal behaviour of spinodal metamaterials generated via the Cahn–Hilliard equation. Their smooth and bi-continuous topology enables seamless tuning of structural anisotropy, making them promising candidates for directional heat transport. However, while their mechanical behaviour has been extensively investigated, their thermal conductive behaviour remains largely unexplored. To address this gap, a finite-element-based computational homogenization framework to evaluate their effective thermal conductivities is presented. A parametric analysis maps thermal conductivity as a function of the design parameters, providing a basis for inverse design. The core contribution of this work is the derivation of a thermomechanical cross-property relation for spinodal metamaterials with a 50–50 composition, providing a direct link between effective thermal conductivity and Young’s modulus. This enables the prediction of thermal properties using more accessible mechanical data. The mechanical and thermal homogenization approaches, along with the derived cross-property relations, are experimentally validated on manufactured samples. Young’s moduli are obtained through compression tests, while thermal conductivities are measured via a steady-state dual-Peltier setup. Overall, this work provides a validated tool for the characterization and inverse design of spinodal thermal metamaterials with extension to additional compositions representing a straightforward generalization of the approach. This tool can be used for efficient thermo-structural optimization by eliminating the need for demanding thermal experiments, allowing designs to be solely based on mechanical analyses, or vice-versa if necessary.