A mechanical metamaterial with adjustable positive to negative Poisson's ratio based on rotating trapeziums and triangles

This paper proposes a metamaterial in which the Poisson's ratio can be tuned from positive to negative for infinitesimal deformation, and can evolve from positive to negative or vice versa for large deformation. Based on a hybrid of rotating trapeziums and triangles, the effective Poisson's ratios of this metamaterial under on-axes loading were obtained by geometrical analysis. The on-axes Young's moduli were established by matching the potential energy stored by the rotational elastic restraint at the hinges with the strain energy of deformation for the homogenised continuum. Results indicate that, at critical internal angles, the metamaterial's Poisson's ratios exhibit sign-switching upon stress direction reversal while the corresponding Young's moduli become extremely large. Results also reveal the existence of terminal states, in the case of large deformation, in which the internal angles no longer change unless the direction of applied load is reversed. This metamaterial is useful for applications whereby material properties are required to change abruptly at certain stages and for applications where the properties can be altered in situ.