Isogeometric shape optimization of smoothed petal auxetics with prescribed nonlinear deformation

Abstract Auxetic materials with negative Poisson’s ratio have potential applications across a broad range of engineering fields. Several FE based design techniques have been developed to achieve auxetic materials with targeted effective properties, mostly in linear deformation regime. In this paper, an isogeometric shape optimization framework for designing 2D auxetic materials with prescribed deformation over large strain intervals is presented. Taking into account practical manufacturing considerations, a minimum thickness for each member is imposed via a spline-based geometric constraint. The capability of the framework is demonstrated through two examples. First, the paper considers shape optimization of smoothed hexa-petals in plane strain condition to achieve constant Poisson’s ratios ranging from a null value to -0.5 to an effective tensile strain of 50%. The second example showcases the shape optimization of smoothed tri- and hexa-petals in plane stress condition for targeted nonlinear deformation behaviour of cat’s skin up to 90% tensile strain.