Non-Linear Matters: Auxetic Surfaces

Auxetic structures exhibiting non-linear buckling are a prevalent research topic in the material sciences due to the ability to tune their reversible actuation, porosity, and negative Poisson’s ratio. However, the research is limited to feature sizes at scales below 10 mm2, and to date, there are no available efficient design and prototyping methods for architectural designers. Our study develops
design principles and workflow methods to transform standard materials into auxetic surfaces at an architectural scale. The auxetic behavior is accomplished through buckling and hinging by subtracting from a homogeneous material to create perforated patterns. The form of the perforations, including shape, scale, and spacing, determines the behavior of multiple compliant "hinges" generating novel patterns that include scaling and tweening transformations. An analytical method was introduced to generate hinge designs in four-fold symmetric structures that approximate non-linear buckling. The digital workflow integrates a parametric geometry model with non-linear finite element analysis (FEA) and physical prototypes to rapidly and accurately design and fabricate auxetic materials. A robotic 6-axis waterjet allowed for rapid production while maintaining needed tolerances. Fabrication methods allowed for spatially complex shaping, thus broadening the design scope of transformative auxetic material systems by including graphical and topographical biases. The work culminated in a large-scale fully actuated and digitally controlled installation. It was comprised of auxetic surfaces that displayed different degrees of porosity, contracting and expanding while actuated electromechanically. The results provide a promising application for the rapid design of non-linear auxetic materials at scales complimentary to architectural products.