Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization

• Published in: Computer methods in applied mechanics and engineering Vol. 323; pp. 250 - 271
• Main Authors: Wang, Zhen-Pei, Poh, Leong Hien, Dirrenberger, Justin, Zhu, Yilin, Forest, Samuel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.08.2017; Elsevier BV; Elsevier
• Subjects: Adjoint method; Auxetic material; Computational periodic homogenization; Condensed Matter; Geometry; Hinges; Homogenization; Isogeometric shape optimization; Isotropy; Materials Science; Negative Poisson’s ratio; Optimization; Petals; Physics; Poisson's ratio; Sensitivity analysis; Shape optimization; Sizing; Sizing constraint; Stress concentration; Studies; Negative Poisson’s ratio; Computational periodic homogenization; Adjoint method; Isogeometric shape optimization; Sizing constraint; Auxetic material
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2017.05.013

An important feature that drives the auxetic behaviour of the star-shaped auxetic structures is the hinge-functional connection at the vertex connections. This feature poses a great challenge for manufacturing and may lead to significant stress concentrations. To overcome these problems, we introduced smoothed petal-shaped auxetic structures, where the hinges are replaced by smoothed connections. To accommodate the curved features of the petal-shaped auxetics, a parametrisation modelling scheme using multiple NURBS patches is proposed. Next, an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance. To ensure a minimum thickness for each member, a geometry sizing constraint is imposed via piece-wise bounding polynomials. This geometry sizing constraint, in the context of isogeometric shape optimization, is particularly interesting due to the non-interpolatory nature of NURBS basis. The effective Poisson ratio is used directly as the objective function, and an adjoint sensitivity analysis is carried out. The optimized designs – smoothed petal auxetic structures – are shown to achieve low negative Poisson’s ratios, while the difficulties of manufacturing the hinges are avoided. For the case with six petals, an in-plane isotropy is achieved.