Thermal conductivity of architected cellular metamaterials

Periodic architected cellular metamaterials, as a novel class of low-density materials, possess unprecedented multifunctional properties mainly due to their underlying microarchitecture. In this paper, we study the thermal conductivity of cellular metamaterials and evaluate their performance for thermal management applications. To understand the relations between the microarchitecture and the thermal response, we analyze the thermal conductivity of a wide range of cellular metamaterials with strategically developed microarchitectures from two-dimensional (2D) cells with Supershape pores to three-dimensional (3D) thin-walled open lattices and shellular materials. We implement standard mechanics homogenization on the periodic representative volume elements (RVEs) of these cellular metamaterials to examine the effect of pore architecture (relative density, pore shape, pore orientation, and pore elongation) on their effective thermal conductivity. The numerical results show how the thermal conductivity of an isotropic material can be modified by pore introduction and how the pore architecture could lead to an anisotropic effective thermal conductivity tensor. To examine the impact of having 2D Supershape cuts on 3D RVEs, thin-walled open lattices are designed as an assembly of thickened 2D RVEs with Supershape pores. A mathematical model is derived based on the effective thermal properties of the constituent 2D RVEs to predict the effective thermal properties of these lightweight cellular materials. Effective thermal conductivity of shellular materials based on triply periodic minimal surfaces is also compared with those of the previously introduced architectures. Unlike the shellular materials, which only cover a narrow region of thermal conductivity versus relative density chart, cellular materials with a wide range of anisotropic effective thermal conductivities can be engineered by using 2D Supershape pores on 2D or 3D thin-walled cells. Finally, we show how the concept of architected functionally graded cellular materials can be used to tune the heat flow within cellular media to guide it in a specific direction to control the temperature inside advanced 3D printed materials. As a case study, the optimum spatial distribution of pore rotation angle is found to maximize or minimize the heat flow passing through different sides of a square-shaped porous slab. This paper opens an avenue for developing thermal metamaterials with programmable anisotropic thermal properties.