Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν∈[−0.78,0.00] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.