A metamaterial with sign-programmable thermal expansivity and Poisson’s ratio constructed from a hybrid of rotating and non-rotating rigid units

Abstract

A 2D mechanical metamaterial is introduced herein using a hybrid of rotating parallelograms and non-rotating rhombi. The in-plane Poisson’s ratio under on-axes loading were derived by considering the rotation of the parallelograms. The on-axes coefficients of thermal expansion were extracted by matching the simple harmonic motion energy with the principle of energy equipartition, while the on-axes Young’s moduli were formulated by equating the total stored rotational spring potential energy at the connecting points with the strain energy of deformation for the equivalent continuum of the metamaterial. Results indicate that the Poisson’s ratio and CTE are primarily governed by the separation angles between the rigid units and, to a smaller extent, by the shapes of the rotating rigid units. In addition to the aforementioned parameters, the effective Young’s moduli of this metamaterial is directly proportional to the rotational elastic restraint at the hinges that connect adjacent rigid units. Due to the instability of the metamaterial under a specific geometrical condition, charges are incorporated into the rhombi in order to programme the sign of the Poisson’s ratio.