Domain-Oriented Hierarchical Topology Optimisation—An Approach for Heterogeneous Materials

In structural topology optimisation, intermediate densities are typically interpreted as local distributions of heterogeneous materials, bridging the gap between a solid and a void through optimised arrangements of cellular or composite microstructures. These multiscale configurations, governed by interactions between micro- and macroscales, are commonly addressed via hierarchical approaches. However, such methods often suffer from high computational cost and limited practical applicability. This work proposes an alternative strategy that reformulates the hierarchical problem by replacing pointwise microscale variations with a subdomain-based formulation. Each subdomain is associated with a periodic microstructure, reducing the number of local problems and significantly decreasing computational demands. A multiscale topology optimisation framework is developed using Asymptotic Expansion Homogenisation, enabling effective macrostructural properties and supporting inverse homogenisation for microscale design. The proposed method is implemented in a user-developed code and validated through several benchmark problems. The results show that the subdomain approach yields discrete and manufacturable microstructures that better reflect real-world composite applications, while also achieving substantial improvements in computational efficiency.