Isogeometric topology optimization for computational design of re-entrant and chiral auxetic composites

Auxetic composites, a kind of rationally artificial materials, possess superior multifunctional properties due to a mixture of materials. In this paper, an Isogeometric Topology Optimization (ITO) method is proposed for computational design of both the re-entrant and chiral auxetic composites in both 2D and 3D. The homogenization is numerically implemented using isogeometric analysis (IGA) to predict macroscopic effective properties of microstructures, where the periodic boundary formulation is imposed. An effective Non-Uniform Rational B-splines (NURBS)-based Multi-Material Interpolation (N-MMI) model is applied to compute material properties of all points in composite microstructures, mainly including the Fields of Design Variables (DVFs), Fields of Topology Variables (TVFs), and multi-material interpolation. A unified ITO formulation is developed for 2D and 3D auxetic composites, where an appropriate objective function with a weight parameter is defined to control the generation of different deformation mechanisms. Finally, several numerical examples are performed to demonstrate the effectiveness of the proposed ITO method, and a series of 2D and 3D auxetic composites with the re-entrant and chiral deformation mechanisms are found. The optimized composite structures are simulated using ANSYS to show the auxetic behavior.