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• Full series of bi-material metaunits were devised, coupled with a vector analysis method to identify the CTE tensors. • A strategy was proposed to design diverse classes of metamaterials integrating multi-directional programmable CTEs. • The mechanical performances of the metamaterials were well theoretically established and customized. • The desirable CTEs and high structural efficiency were synergistically achieved in the devised metamaterials. • A general principle was identified to guide the further development of new metamaterials. Metamaterials, incorporating specific micro-architectures, could be purposely customized to export the programmability in both thermal expansional and mechanical performances, which are beneficial to obtain the thermal and structural stabilities in engineering devices. Here, by focusing on developing an original design strategy, multiple classes of metamaterials were devised and analyzed to integrate the programmable coefficient of thermal expansion (CTE) and mechanical performances (relative density, stiffness and strength). In detail, firstly, a series of the bi-material metaunits was devised, and a vector analysis method was proposed to analytically identify the CTE tensors. Then, an original design strategy, i.e., matrix transformation method, was developed to systematically devise multiple classes of 3D metamaterials with the unidirectional, transversal isotropic and isotropic CTEs. Besides, the mechanical performances, including the relative density, stiffness and strength, were theoretically established. It was identified that these metamaterials well balanced the directionality and programmability of the CTEs. Most importantly, by modulating the geometrical parameters, the desirable CTEs, light weight, high stiffness and strength could be synergistically achieved in these metamaterials. Eventually, a principle was established to guide the development of metamaterials. That was the original design strategy acted as the underlying foundation to map the specific architectures in metamaterials, correspondingly, to build the ability to synergistically program or customize the thermal expansional and mechanical performances. [ABSTRACT FROM AUTHOR]