Supplementary material from "Hard-Particle rotation enables soft-hard integrated auxetic mechanical metamaterials"

An auxetic design is proposed by soft-hard material integration and demonstrate negative Poisson's ratio (NPR) can be achieved by leveraging unique rotation features of non-connected hard particles in a soft matrix. A theoretical mechanics framework that describes rotation of hard particles in a soft matrix under a mechanical loading is incorporated with overall Poisson's ratio of the soft-hard integrated metamaterials. The theoretical analysis shows that the auxetic behaviour of the soft-hard integrated structures not only relies critically on geometry of particles, but will also depends on their periodic arrangements in the soft matrix. Extensive finite-element analyses (FEA) are performed and validate the theoretical predictions of hard-particle rotation and overall Poisson's ratio of soft-hard integrated structures. Furthermore, uniaxial tensile tests are carried out on 3D printed soft-hard integrated structures and confirm auxetic behaviour of soft-hard integrated structures enabled by the rotation of hard particles. Besides, Poisson's ratio varies nonlinearly with the thickness of specimens and reaches a maximum NPR far out of the bounds of plane stress and plane strain situations, which agrees well with FEA. This work provides a theoretical foundation for the design of mechanical metamaterials enabled by soft-hard material integration with auxetic deformation behaviour.