Micro- and Macro-Scale Topology Optimization of Multi-Material Functionally Graded Lattice Structures

Abstract

Lattice structures are becoming an increasingly attractive design approach for the most diverse engineering applications. This increase in popularity is mainly due to their high specific strength and stiffness, considerable heat dissipation, and relatively light weight, among many other advantages. Additive manufacturing techniques have made it possible to achieve greater flexibility and resolution, enabling more complex and better-performing lattice structures. Unrestricted material unit cell designs are often associated with high computational power and connectivity problems, and highly restricted lattice unit cell designs may not reach the optimal desired properties despite their lower computational cost. This work focuses on increasing the flexibility of a restricted unit cell design while achieving a lower computational cost. It is based on a two-scale concurrent optimization of the lattice structure, which involves simultaneously optimizing the topology at both the macro- and micro-scales to achieve an optimal topology. To ensure a continuous optimization approach, surrogate models are used to define material and geometrical properties. The elasticity tensors for a lattice unit cell are obtained using an energy-based homogenization method combined with voxelization. A multi-variable parameterization of the material unit cell is defined to allow for the synthesis of functionally graded lattice structures.