Concurrent multiscale topology optimization for size-dependent structures incorporating multiple-phase materials

The significant progress in additive manufacturing has resulted in the development of well-engineered microstructures with innovative topological configurations, showcasing exceptional performance across diverse fields. Topology optimization is widely recognized as an advanced design tool that provides engineers with new insights for creating lightweight structures. As integration devices continue to trend towards miniaturization, the size effect in small-scale structures remains a persistent challenge. The absence of characteristic parameters to describe this size effect hinders proper explanation through traditional multiscale topology optimization based on classical mechanics. Therefore, we propose a size-dependent topology optimization framework for concurrent multiscale design involving multiple-phase materials. The modified couple stress theory is proposed to account for the size effect in small-scale structures. The numerical findings suggest that the size effect is significantly influenced by the ratio of elastic modulus, volume fraction, and width-to-length ratio of the representative volume element as its characteristic size approaches the length of the material. These results highlight the importance of considering size-dependent effects in topology optimization for multiscale design and provide valuable insights for engineers and researchers in this field. •Topology optimization for structures considering multiple-phase materials and size effect is constructed.•The modified couple stress theory is proposed to capture the size effect in small-scale structures.•The size effect becomes increasingly significant as the characteristic size approaches the length of the material.