A Negative Thermal Expansion Metamaterial Inspired by the Sicilian and Manx Symbols

Abstract

A negative thermal expansion (NTE) metamaterial is established herein by inspiration from the Sicilian and Manx symbols to form rigid units of the metamaterial. By attaching connecting material of positive thermal expansion to the rigid units, the resulting metamaterial exhibits NTE. Analytical forms for the effective coefficients of thermal expansions (CTE) were established using infinitesimal and finite deformation assumptions for small and large temperature changes, respectively. Results indicate that the negativity of this metamaterial’s thermal expansion is enhanced with the thickness of the connecting material but decreases with the dimensions of the rigid units. The transverse isotropy for this metamaterial’s CTE is useful if thermal expansion compensation is required in two orthogonal directions but zero thermal expansion is required in the remaining orthogonal direction.