Design optimization of multifunctional metamaterials with tunable thermal expansion and phononic bandgap

Metamaterials have been extensively investigated owing to their unusual properties. However, the design of multifunctional metamaterials requires further investigation. This study focused on the design of three-dimensional (3D) metamaterials to achieve tunable negative thermal expansion and phononic bandgap properties. First, the independent continuous mapping (ICM) topology optimisation method was applied to create metamaterial microstructures with negative thermal expansion properties based on the multi-scale asymptotic homogenisation theory. Secondly, the conceptual structure from the topology optimisation was reconstructed and parameterized to achieve the desired phononic bandgap widths under negative thermal expansion, using a surrogate model-based optimisation method. Both the negative coefficient of thermal expansion and phononic bandgaps were verified through numerical simulations. The results reveal that, by selecting appropriate parameters, the designed metamaterials can have both a negative coefficient of thermal expansion and a maximum bandgap width ratio. The proposed method provides an important reference for the rational design of multifunctional metamaterials.