Isogeometric Density Field Method for Topology Optimization of Micro-architected Materials

In this paper, an isogeometric density field method is proposed for the design of micro-architected materials with the specific mechanical properties, consisting of the maximum bulk and shear modulus and the Negative Poisson's ratio (NPR). Firstly, the non-uniform rational B-splines (NURBS) basis functions are employed to construct the density field function (DFF), where the Shepard function is used to improve the smoothness of the nodal densities assigned to control points. The NURBS basis functions and the Shepard function can ensure the sufficient continuity and smoothness of the DFF, owing to their significant properties. The optimization formulation for micro-architected materials is developed using the DFF, where the isogeometric analysis (IGA) is applied to evaluate the unknown structural responses. Effective macroscopic properties of materials are predicted by the asymptotic homogenization method. The same NURBS basis functions used in the IGA and the DFF can keep the consistency of the geometric model and analysis model, which provides the unique benefits. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach for micro-architected materials.