Controllable optimal design of auxetic structures for extremal Poisson’s ratio of −2

Abstract

We develop a lattice structure of a desired Poisson’s ratio that is maintained when subjected to finite deformation. Using a gradient-based design optimization in an isogeometric computational framework, the representative unit cell is sophisticatedly tailored to attain the controlled Poisson’s ratio of up to −2. The ligaments of the lattice structure are modeled using geometrically exact beams whose configuration and cross-sectional area are regarded as design variables, which are parameterized by the higher order B-spline basis functions. The obtained optimal design is fabricated using a PolyJet 3-D printing machine and validated by physical experiments. Excellent quantitative agreement is observed between the numerical and the experimental results measured from an optical deformation measurement system.