Thermo-mechanical performance of two-dimensional porous metamaterial plates

Metamaterials belong to a relatively new class of materials, whose physical properties derive from the mesostructure and spatial arrangement of the constituent unit cells rather than from their composition and chemical structure. By properly organizing their topology in the two-dimensional (2D) or three-dimensional (3D) space, metamaterials offer new possibilities for developing materials with unprecedented physical properties (mechanical, thermal, acoustic, optical, etc.). In several real applications, such as components for building insulation, the thermal and mechanical performances need to be tailored and optimized at the same time. In the present paper, the response of 2D porous metamaterial (metaplate) is analyzed from a double perspective. Firstly, the thermal response, quantified by the heat flux-resulting from a fixed temperature gradient - which is related to the thermal resistance of the plate, is studied. From another perspective, the mechanical stiffness of the plate has been examined. Both regular and random void patterns as well as pore with various shapes and sizes are considered as design parameters of the metaplate. An analytical model, based on the geometrical tortuosity of the porous domain is presented for predicting the thermal response. The study provides a new perspective on the design of metaplates with a fixed porosity, whose pores' geometry and arrangement can be tuned in order to accomplish a desired thermal and mechanical response at the same time.