Analytical Model of Temperature-Induced Deformation for Tunable Thermal Expansion Metamaterial.

Tunable thermal expansion metamaterials exhibit superior shock absorption performance in the field of high-precision equipment, but the applications are currently restricted by the unclear quantitative relationship of temperature-induced deformation. Herein, this work leverages the virtual work principle and the deformation geometric relationship to establish a generic temperature-induced deformation control model for bi-materials by utilizing the key variable coverage ratio under the condition of no deformation in the vertical direction. The feasible region regarding flexibility for the internal serpentine unit and lattice structure with different coverage ratios is given. The combination of the finite element and experimental methods is adopted to examine temperature-induced deformation, which presents tunable thermal expansion performances associated with the coverage ratio and temperature. This work, based on the established deformation coordination relationship of dual-material temperature-sensitive metamaterials, achieves temperature-induced deformation control and provides a reference for structural design adaptable in various working conditions such as vibration isolation and vibration reduction in complex engineering such as aerospace and so on. By strategically designing the coverage of the two structures within the specified range to maintain equivalent flexibility, the ultimate deformation of the serpentine unit is reduced by one-half due to deformation induced by temperature variations.