Isogeometric shape optimization of smoothed petal auxetics with prescribed nonlinear deformation

• Published in: Computer methods in applied mechanics and engineering 2019-11, Vol.356, p.16-43
• Main Authors: Pokkalla, Deepak Kumar, Wang, Zhen-Pei, Poh, Leong Hien, Quek, Ser Tong
• Format: Article
• Language: English
• Subjects: Auxetic; Auxetic materials; Deformation effects; Electrons; Geometric constraints; Isogeometric analysis; Negative Poisson’s ratio; Optimization; Petals; Plane strain; Plane stress; Poisson's ratio; Sensitivity analysis; Shape optimization; Skin; Tensile strain
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.07.014

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. •Shape optimization with IGA for smoothed petals with targeted deformation.•Minimum member thickness enforced with a spline based constraint.•Constant negative Poisson’s ratio achieved for up till 50% effective tensile strain in plane strain.•Replicated nonlinear deformation of cat’s skin up to 90% tensile strain.