Introducing material-specific stress constraints in multi-material topology optimization

Multi-material topology optimization has emerged as a powerful design tool, enabling the integration of different material properties to enhance structural performance. A critical challenge in applying stress constraints to multi-material structures is that each material has a distinct stress limit that must not be exceeded. Conventional approaches typically address this by enforcing a single stress limit for all materials or using interpolation functions, both of which introduce limitations and additional complexities. In contrast, we propose a material-specific stress constraint method that treats each material separately. The stress in each material is computed individually and directly compared to its respective stress limit, eliminating the need for additional interpolation functions. Furthermore, the stress singularity phenomenon is naturally avoided without requiring relaxation techniques. To solve the optimization problem, an image regeneration approach based on CNN is employed. A projection filter is developed that strictly enforces the mass constraint while ensuring a valid material distribution. The method is evaluated through three numerical examples, demonstrating the impact of stress constraints on the minimum compliance problem. The results show a significant reduction in stress levels, in exchange for a small increase in compliance, while ensuring that the stress in all materials remains within their respective limits.