Microstructural Effects on the Poisson's Ratio of Star‐Shaped Two‐Dimensional Systems

Microstructured plates, consisting of various conventional and re‐entrant cells, are numerically constructed and analyzed for their effective elastic properties under in‐plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two‐dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus.