Auxetic properties of a tangram-inspired metamaterial

Abstract

AbstractThis paper explores a new anisotropic auxetic system that consists of rotating rhombi and right triangles by inspiration from tangram pieces. The Poisson’s ratio was developed by geometrical analysis on the representative unit with prescribed boundary requirements. Upon assigning rotational stiffness to the hinges, the Young’s modulus was established by matching the potential energy stored in the spiral springs with the strain energy of the deformation for the homogenized continuum. Results indicate that the on-axes Poisson’s ratio and dimensionless Young’s moduli are governed by the shapes and separation angles of the rigid units which, in turn, determine the dimension of the representative unit of the metamaterial. For the special case where the Poisson’s ratio is −1 when stretched on either axis, the Young’s moduli are equal. For this special case, the separation angles and the on-axes Young’s moduli increase monotonically with the shape descriptor of the rigid units. The capability of combining rotating rigid units of quadrilateral and triangular shapes suggests that new combinations of mechanical properties can be designed from rotation-based auxetic systems.