Metamaterials with Poisson's ratio discontinuity by means of fragmentation–reconstitution rotating units

This paper presents for the first time two types of metamaterials based on the fragmentation–reconstitution of rotating units in order to produce Poisson's ratio discontinuity at the original state. For both metamaterials, each rotating unit takes the form of a rhombus that comprises eight sub-units. During on-axis stretching, each rhombus fragments into eight rotating sub-units. When the prescribed strain is reversed, these eight sub-units reconstitute back into a single rotating rhombus such that they rotate as a rigid body. Using geometrical construction, the incremental Poisson's ratio was established at the original state. In the case of large deformation, the finite Poisson's ratio was formulated in conjunction with the maximum allowable rotations for full stretching along both axes and for full compression. The family of on-axes Poisson's ratio versus rotational angles for various shape descriptors displays a fork-shaped distribution with discontinuity at the original state. Two major distinguishing factors of these metamaterials—property discontinuity at the original state with constant and variable Poisson's ratio under compression and tension, respectively—allow them to function in ways that cannot be fully performed by conventional materials or even by auxetic materials and metamaterials.