An anisotropic negative thermal expansion metamaterial with sign-toggling and sign-programmable Poisson’s ratio

A mechanical metamaterial is introduced herein by drawing inspiration from an Aztec geometric pattern. This metamaterial deformation mechanism for Poisson’s ratio and Young’s modulus is based on non-rotating rhombi with rotating triangles, and while the shear modulus analysis herein is based on rotating rhombi with non-rotating triangles, hence “partially rotating rigid units”. The coefficient of thermal expansion was obtained by equating the potential energy expressions from the simple harmonic motion and from the principle of energy equipartition, while the effective Young’s modulus was acquired by equating the strain energy from rotational stiffness with that from the strain energy of deformation from an assumed homogenised continuum. Due to the zero and extreme Poisson’s ratio based on infinitesimal deformation, the finite approach was employed. Results indicate that the proposed metamaterial exhibits anisotropic negative thermal expansion with sign-switching Poisson’s ratio when applied stress along one axis is reversed. The Poisson’s ratio for loading in another axis is undefined under tension but can be programmed to exhibit either sign when compressed. The Young’s modulus is directly governed by the rotational stiffness and strongly influenced by the extent of rotation, followed by the aspect ratio of the rotating units. Due to its uniqueness, the currently considered mechanical metamaterial can be used under specific requirements which are difficult to be attained by other materials with negative properties.