Synergistically program thermal expansional and mechanical performances in 3D metamaterials: Design-Architecture-Performance

•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 .