Porous materials with high negative Poisson’s ratios—a mechanism based material design

In an effort to tailor functional materials with customized anisotropic properties-stiffness and yield strain, we propose porous materials consisting of flexible mesostructures designed from the deformation of a re-entrant auxetic honeycomb and compliant mechanisms. Using an analogy between compliant mechanisms and a cellular material's deformation, we can tailor the in-plane properties of mesostructures; low stiffness and high strain in one direction and high stiffness and low strain in the other direction. An analytical model is developed to obtain the effective moduli and yield strains of the porous materials by combining the kinematics of a rigid link mechanism and deformation of flexure hinges. A numerical technique is implemented with the analytical model for the nonlinear constitutive relations of the mesostructures and their strain-dependent Poisson's ratios. A finite element analysis (FEA) is used to validate the analytical and numerical models. The designed moduli and yield strain of porous materials with an aluminum alloy are 2 GPa and 0.28% in one direction and 0.2 MPa and 28% in the other direction. These porous materials with mesostructures have high negative Poisson's ratios, v(xy)* down to -82 due to the large rotation of the link member in the transverse direction caused by the input displacement in the longitudinal direction. The porous materials also show higher moduli for compressive loading due to the contact of flexure hinges. This paper demonstrates that compliant mesostructures can be used for next-generation material design in terms of customized mechanical properties; modulus, strength, strain, and Poisson's ratio. The proposed mesostructures can also be easily manufactured using a conventional cutting method.