Multi-scale and multi-material topology optimization of gradient lattice structures using surrogate models

Abstract

Lattice structures have received considerable attention in the recent years due to the increasingly high flexibility and resolution offered by additive manufacturing techniques. They also present an attractive design approach for applications such as aerospace and biomedical engineering due to their desirable properties including lightweight, high specific strength and stiffness and heat dissipation. This work explores a computationally efficient topology optimization approach while increasing the flexibility of a restricted unit cell design. Unrestricted material unit cell designs are often associated with high computational power and connectivity problems, while highly restricted lattice unit cell designs may lack the potential to reach the optimal desired properties at a reduced computational effort. A two-scale concurrent optimization of lattice structure is proposed in this study, where the topology optimization at the macro-scale structure and the underlying material micro-structures is performed simultaneously to achieve optimal topologies. Surrogate models are used to represent material and geometrical properties for a continuous topology optimization approach. An energy-based homogenization method combined with voxelization is employed to obtain the elasticity tensors for a lattice unit cell library. A multi-variable parameterization of the material unit cell is defined, which allows for the synthesis of functionally graded lattice structures. A multi-material extension to the concurrent multi-scale topology optimization is also explored. The performance of the optimized graded lattice structure is compared to a uniform lattice structure.