Stiffness characteristics for a series of lightweight mechanical metamaterials with programmable thermal expansion

The stiffness characteristic is of significance for the mechanical metamaterials under the mechanical loading. This work explores the stiffness characteristics for a series of lightweight mechanical metamaterials with unique programmability in the coefficient of thermal expansion (CTE). The effective stiffness is analytically established considering both stretching and bending deformations. The numerical modeling verifies the theoretical analysis. By rationally modulating the cell architectures, the programmable CTE ranged from negative to positive values and the lightweight is realized. Besides, the high specific stiffness could be achieved. Especially, the metamaterials VS and VH present superior specific stiffness. The coupling relationships of the stiffness, density and CTE are identified, and the high specific stiffness and low CTE can be obtained in the vertex-connected metamaterials, which benefits the dimensional stability controlling. Both large CTE and high specific stiffness are achieved in the metamaterial SH. Moreover, the comparisons with the commonly available materials identify that the metamaterials integrate the considerable stiffness and lightweight performances, as well as an exclusive function of programmable CTE. The analysis of the stiffness characteristic is expected to guide the applications of the metamaterials in engineering where the control of CTE, requirements of both lightweight and high stiffness should be strictly fulfilled.