Cellular Materials With Extremely High Negative And Positive 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 in-plane properties of mesostructures; low stiffness and high strain in one direction and high stiffness and low strain in the other direction. Two mesostructures based on hexagonal honeycombs with positive and negative cell angles are generated. An analytical model is developed to obtain 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 to the analytical model for 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 model. The moduli and yield strain of a porous aluminum alloy are about 6.3GPa and 0.26% in one direction and about 2.8MPa and 12% in the other direction. The mesostructures have extremely high positive and negative Poisson's ratios, v(xy)* (similar to +/- 40) due to the large rotation of the link member in the transverse direction caused by the input displacement in the longitudinal direction. The mesostructures also show higher moduli for compressive loading due to the contact of slit edges at the center region. This paper demonstrates that compliant mesostructures can be used for a next generation material design in terms of tailoring mechanical properties; moduli, strength, strain, and Poisson's ratios. The proposed mesostructures can also be easily manufactured using a conventional cutting method.