Hard-particle rotation enabled 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 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 three-dimensional 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.