Adjustable positive and negative hygrothermal expansion metamaterial inspired by the Maltese cross

A metamaterial that can manifest both positive and negative coefficients of moisture and thermal expansion is presented herein, based on inspiration from the Maltese cross. Each unit of the metamaterial consists of a pair of equal-armed crosses pin-joined at their junctions to permit rotation, but elastically restrained by a bimaterial spiral spring, and four pairs of hinge rods to translate the relative rotational motion of the pair of equal-armed crosses into translational motion of the connecting rods. The effective coefficients of moisture and thermal expansion models were developed for small and large changes in the hygrothermal conditions using infinitesimal (approximate) and finite (exact) motion analyses, respectively, with the former giving constant effective coefficients with respect to environmental changes. Results indicate that the approximate method underestimates the magnitude of both the effective expansion coefficients under cooling and drying but overestimates magnitudes of both coefficients during heating and moistening, and that the change in both expansion coefficients is more drastic during cooling and drying than during heating and moistening. In addition to providing another micro-lattice geometry for effecting expansion coefficients of either signs, this metamaterial exhibits auxetic property.