Isogeometric topology optimization for rational design of ultra-lightweight architected materials

Architected materials with the desirable properties, such as the lightweight and the superior stiffness, have accepted considerable attention in recent years. This paper aims to study the design of architected materials but with the ultra-lightweight using an effective and efficient Isogeometric Topology Optimization (ITO) method. An enough smooth and continuous Density Distribution Function (DDF) is constructed using the Shepard function and NURBS basis functions, to describe the topology of the micro-architecture. Later, the homogenization with a simple periodic boundary formulation is numerically implemented by isogeometric analysis (IGA) to predict effective macroscopic properties using the micro information. An ITO formulation with the specific objective function is developed to rationally design 2D and 3D architected materials with the extreme elastic properties using the DDF and IGA-based homogenization, in which the volume fraction needs to be very low to ensure the optimized micro-architectures with the ultra-lightweight. NURBS basis functions offer a unified formula for the structural geometry, the solution space and the micro topology in architected materials. Finally, several numerical examples are provided to display the effectiveness of the ITO method for the ultra-lightweight architected materials, particularly for 3D scenario. A series of novel and interesting 3D ultra-lightweight architected materials are found, which are also prototyped using the Selective Laser Sintering (SLS) technique.