Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints

• Published in: Computer methods in applied mechanics and engineering 2019-02, Vol.344, p.334-359
• Main Authors: Cheng, Lin, Bai, Jiaxi, To, Albert C.
• Format: Article
• Language: English
• Subjects: Additive manufacturing; Algorithms; Asymptotic methods; Density; Design optimization; Elastic properties; Elasticity; Energy absorption; Functionally gradient materials; Homogenization; Interpolation; Lattice design; Lattice structure topology optimization; Mathematical models; Mechanical properties; Sensitivity analysis; Stiffness; Stress constraint; Topology optimization; Weight; Yield criteria; Yield strength; Yield stress
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.10.010

Advances in additive manufacturing (AM) have drawn considerable interest due to its ability to produce geometrically complex structure, such as lattice materials. In this work, a novel methodology is proposed to design graded lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structure design with predictable yield performance. Instead of using the power law of material interpolation in the SIMP method, asymptotic homogenization method is employed to compute the effective elastic properties of lattice material in terms of design variable, i.e. relative density. For yield strength, a multiscale failure model is proposed to capture yield strength of microstructure with macroscopic stress. At macroscale, a modified Hill’s yield criterion is employed to describe anisotropic yield strength of lattice material. The material constants in Hill’s model are assumed to be a function of relative density, and thus a model is built up to formulate yield strength of lattice structure with macroscopic stress. The experimental verification on the printed samples demonstrates that both the homogenized elastic model and yield model can accurately describe the elasticity and plasticity of the lattice structure. Based on the proposed material interpolation for lattice structure, a lattice structure topology optimization framework is proposed for minimizing total weight of the structure under stress constraint. The sensitivity analysis is performed for the implementation of the optimization algorithm. Two three-dimensionally numerical examples are performed to demonstrate the effectiveness of the proposed optimization method, as well as accuracy of the proposed homogenization technique for graded lattice structure design. Experiment is conducted to systematically examine yielding of the optimally graded lattice structure design and compare its performance with a uniform structure. It is found that the proposed optimization framework is valid for the design examples examined and can significantly enhance mechanical performance of the structure (i.e. yield loading, stiffness, energy absorption, etc.)