Low frequency bandgap and high stiffness of innovative auxetic metamaterial with negative thermal expansion

Achieving multifunctional integration is crucial in mechanical metamaterials to meet the requirements of structures and equipment serving in complex environments across various engineering fields. In this study, we propose two novel bi-material and tri-material metamaterials based on the original edge-shared quadrangle (EQ/EQO) metamaterial, which exhibit negative thermal expansion (NTE), negative Poisson's ratio (NPR), and bandgap characteristics. The effective thermoelastic properties, including coefficient of thermal expansion (CTE), Poisson's ratio (PR), and Young's modulus, are compared and analyzed through theoretical formulation based on Timoshenko beam theory and numerical simulation using continuum elements with Abaqus. Additionally, finite element analysis is employed to calculate the energy band structures of these metamaterials based on Bloch's theorem, while the transmission characteristic curve verifies the validity of the obtained band structure. We systematically discuss the bandgap characteristics, coupling relationship between bandgaps and thermoelastic properties, as well as the influence of geometrical parameters on both bandgaps and thermoelastic properties. Our results demonstrate that the effective thermoelastic properties of these metamaterials are primarily determined by their frame structure's geometrical parameters, particularly the incline angle. Furthermore, for bi-material metamaterials, their specific stiffness closely relates to their bandgaps; however, for tri-material metamaterials, only the central local resonant unit determines their bandgap behavior. Notably, planar and 3D tri-material metamaterials can concurrently achieve a low-frequency bandgap along with high stiffness as well as NTE/NPR behavior. This work presents a new design strategy for optimizing multifunctional metamaterials' bandgaps while incorporating NTE behavior.