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.

刚度特性对于机械载荷下的机械超材料具有重要意义。这项工作探索了一系列在热膨胀系数 (CTE) 方面具有独特可编程性的轻量级机械超材料的刚度特性。考虑拉伸和弯曲变形，通过分析建立有效刚度。数值模拟验证了理论分析。通过对单元架构的合理调制，实现了从负值到正值的可编程CTE，实现了轻量化。此外，可以实现高比刚度。特别是，超材料 VS 和 VH 表现出优异的比刚度。确定了刚度、密度和 CTE 的耦合关系，在顶点连接的超材料中可以获得高比刚度和低CTE，这有利于尺寸稳定性控制。在超材料 SH 中实现了大 CTE 和高比刚度。此外，与常用材料的比较表明，超材料集成了相当大的刚度和轻量化性能，以及可编程 CTE 的独特功能。刚度特性的分析有望指导超材料在工程中的应用，其中应严格满足 CTE 控制、轻量化和高刚度要求。此外，与常用材料的比较表明，超材料集成了相当大的刚度和轻量化性能，以及可编程 CTE 的独特功能。刚度特性的分析有望指导超材料在工程中的应用，其中应严格满足 CTE 控制、轻量化和高刚度要求。此外，与常用材料的比较表明，超材料集成了相当大的刚度和轻量化性能，以及可编程 CTE 的独特功能。刚度特性的分析有望指导超材料在工程中的应用，其中应严格满足 CTE 控制、轻量化和高刚度要求。