Optimal design of cavity-free mechanical metamaterials exhibiting negative thermal expansion

In this study, we present a novel topology-optimized design of a two-dimensional cavity-free mechanical metamaterial with a negative coefficient of thermal expansion. We challenge the prevailing hypothesis that cavities are necessary for achieving negative coefficients of thermal expansion. The proposed metamaterial is a periodic lattice of a topology-optimized unit cell comprising three distinct solid materials, analyzed using a homogenization method. To confirm the negative thermal expansion of the optimized structures, we present some numerical experiments of the optimized designs and analyze the deformation of the metamaterial under temperature variations.