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

•The programmable CTE ranging from positive to negative values and low relative density can be realized with the designed metamaterials.•The effective uniaxial stiffness of the metamaterials is theoretically established and numerically validated.•The coupling relationships of stiffness, relative density and programmable CTE are initially revealed and depicted.•The exclusive integrated functions of the metamaterials including low density, considerable stiffness and programmable CTE are superior compared with those of common materials.