Three-dimensional graded metamaterials with customizable thermal responses under space-variant temperature stimuli

Metamaterials with customizable thermal expansions are desirable for important engineering applications. However, existing metamaterials were designed by considering uniform temperature distributions. In the current study, a new design strategy is proposed to develop metamaterials with customizable thermal deformations under space-variant temperature (SVT) stimuli which are non-uniform. Three types of bi-material pyramidal units are first devised through using different material distributions and geometrical configurations. The coefficients of thermal expansion (CTEs) of these units are derived in closed-form expressions. Graded metamaterials are then constructed from the pyramidal units through combined periodic and graded tessellations. Based on targeted thermal deformations under prescribed stimuli, geometrical parameters are identified, and the thermal strains are determined using the newly derived analytical formulas and finite element simulations. The two sets of predictions are found to agree well, which indicates the effectiveness of the new design strategy for the graded metamaterials. The numerical results reveal that the graded metamaterials exhibit customizable uniform deformations under the SVT stimuli. In addition, targeted customizable thermal deformations with quadric-shape strain profiles are achieved in the graded metamaterials. Compared with the conventional design with uniform temperature distributions, the newly proposed design of metamaterials under non-uniform SVT stimuli is more versatile and flexible, thereby providing a systematic strategy for developing graded metamaterials.