Novel metamaterial structures with negative thermal expansion and tunable mechanical properties

The thermal expansion and stiffness characteristics are significant in determining the responses of lightweight mechanical metamaterials in a thermal environment. This paper proposed a novel trapezoid unit with negative thermal expansion (NTE) by three conventional materials with positive thermal expansion, and constructed a series of lightweight metamaterials by sharing edges and sharing vertexes. The effective linear coefficients of thermal expansion (CTE) of these metamaterial structures are theoretically explored by considering axial and bending deformations. Based on Euler beam theory, the effective linear elastic stiffnesses of these metamaterials are given accurately by the stiffness matrix method. The accuracy of the theoretical effective CTE and stiffness is well verified by numerical modeling. The effective linear CTE, elastic stiffness, and Poisson's ratio of these metamaterials can be programmable by controlling geometrical parameters and material properties. The NTE effect can be achieved in ET, EQ, EH, and VT metamaterials due to the presence of re-entrant structures, in which the ET metamaterial can fulfill the maximum magnitude NTE. The NTE and negative Poisson's ratio can simultaneously be realized in EQ metamaterial. Significantly, a broader range of CTE from negative to positive values can be fulfilled in these metamaterials compared with the conventional triangle unit. Furthermore, the high specific stiffness with extremely low thermal stress can be obtained in EQ, VT, and VH metamaterials, which benefits the stability controlling and enhancing natural frequencies of structures in a thermal environment.