Multi-scale topology optimization of multi-material heterogeneous microstructures based on deep learning

Abstract In recent years, although deep learning (DL) has been a powerful tool for accelerating the design of multiscale structures, the existing research focuses on the single-material structural design, and it has not yet proposed an effective solution in the design of multi-material and multi-scale structures. To address this limitation, we introduce a novel multi-material multi-scale topology optimization framework based on deep learning, termed MMTO-DL, specifically tailored for designing multi-material multi-scale structures. The MMTO-DL framework leverages the level set method to implicitly represent heterogeneous microstructures. Each microstructure is governed by height and material variables, which respectively control the configuration and material selection. Furthermore, MMTO-DL incorporates two neural networks for neural reparametrization and surrogate models respectively. The input to the reparametrization network comprises spatial point coordinates within the design domain, while the outputs are sets of height and material variables. Innovatively, MMTO-DL introduces a penalty factor into the Softmax function to prevent the formation of mixed material units, facilitating the regional distribution of multi-material structures. Additionally, a separate neural network is used to build a high-precision surrogate model linking height variables and mechanical properties, substantially cutting computational needs for microstructure analysis. The MMTO-DL framework facilitates sensitivity analysis and gradient information acquisition. The framework’s effectiveness and flexibility are demonstrated through numerical examples involving compliance minimization and shape matching problems.