An isogeometric approach to topological optimization design of auxetic composites with tri-material micro-architectures

Abstract Auxetic composites, which can be viewed as a type of rationally man-made meta-composites with Negative Poisson’s Ratios (NPRs), have received widespread discussions and applications because of the promising, multifunctional and advanced properties. Micro-architectures work as building blocks of unit cells to make up composites, which possess complex topologies of auxetic multi-material. However, it should be noted that a computational design approach with the reasonability and powerful capability of optimizing auxetic composites cells-by-cells is still in need, particularly for composites with three or more materials. In this study, the main focus is to develop an effective and efficient computational design framework for auxetic composites with the tri-material using Isogeometric Topology Optimization (ITO) method, in which a tri-material topology representation model is constructed by non-uniform rationally B-splines (NURBS) to effectively represent micro-structural topology with clear and smooth boundaries. Numerical examples are discussed to present the effectiveness of the computational design framework, where a series of novel and interesting auxetic micro-architectures with the re-entrant or chiral deformation mechanisms can be found. The significance of the current work contributes to developing a platform that enables a scientific design of auxetic composites, rather than heavily depending on human intuition.