Quasi-isotropic metamaterials with negative thermal expansion designed via topology optimization using topological derivative

Designing structures with negative thermal expansion coefficients, which contract when heated, is a significant focus in structural optimization research. While isotropy, meaning uniform properties in all directions, is beneficial for such structures in terms of design flexibility and simulation simplicity, negative thermal expansion structures often exhibit anisotropic, direction-dependent behavior. This study presents a multimaterial topology optimization for structures with a negative quasi-isotropic thermal expansion coefficient. By utilizing a cell structure exhibiting hexagonal symmetry, the approach ensures “quasi-isotropy”, referring to the behavior of a composite material that closely approximates isotropy in certain physical properties. Additionally, the proposed method enhances structural performance through topology optimization employing topological derivatives. Numerical experiments validate the effectiveness of the proposed method, confirming its ability to produce structures with high structural performance and desired thermal expansion properties while maintaining isotropic characteristics. The presented approach offers a novel and promising tool for designing innovative materials and structures with tailored thermal expansion behavior. • Topology optimization method for metamaterials of quasi-isotropic negative thermal expansion. • Optimized through topological derivative-based topology optimization. • Quasi-isotropy is achieved using hexagonal and triangular unit cell.