Mechanical performances and coupling design for the mechanical metamaterials with tailorable thermal expansion

Mechanical performances are of significance for the mechanical metamaterials with the tailorable coefficient of thermal expansion (CTE), when they are in service of mechanical loading. Hence, this work presents the analysis of the mechanical performances for a series of lightweight metamaterials with a wide range of tailorable CTEs. The closed-form expressions of the stiffness, yield/buckling strengths, failure modes and criteria are analytically established. It is revealed that the enhanced mechanical performances including high stiffness and strength can be obtained through reasonably modulating the cell geometries and base materials. In particular, the metamaterials in the Category A present the excellent geometrically independent yield and buckling strengths. The failure modes and corresponding criteria are originally identified especially considering the complicated loadings, geometries and base materials. These failure criteria provide references to the allowable loads to avoid the potential failure. More importantly, the coupling design of the tailorable CTE, relative density, stiffness and strength performances further reveals that the metamaterials are suitable for fulfilling various customized requirements in engineering applications. Particularly, the metamaterial BH satisfies the usage situation that requires low CTE, low density, high stiffness and strength. The analysis of the mechanical performances enhances the engineering applications of these metamaterials when both the function of tailorable CTE and mechanical capacities are in urgent need.