Data-driven topology optimization of mechanical metamaterials via deep neural network and material-field function

Data-driven methods offer an innovative way to explore high-performance mechanical metamaterials, accelerating their engineering applications. However, most existing approaches use image pixel values (e.g. element densities) as input, leading to the curse of dimensionality, resulting in high storage, memory demands, computational costs, and long training times. This article presents a novel lightweight data-driven approach using the material field series expansion (MFSE) function and deep neural network (DNN) to non-iteratively design optimal mechanical metamaterials. By describing material distribution with a material-field function instead of elemental densities, the number of design variables is significantly reduced. A multi-layer perceptron was trained to map coefficients to boundary conditions, with principal component analysis (PCA) applied to reduce the output dimensions. Once trained, the approach instantly generates topology optimization designs for metamaterials, optimizing bulk modulus, shear modulus, or minimizing Poisson's ratio (PR), as demonstrated through numerical examples. The proposed method achieves high accuracy with a minimal amount of training data. Compared to density-based models, the MFSE-DNN method significantly reduces design variables and training time, allowing training on personal PCs with lower computational resources. The proposed method is not limited to the studied metamaterial and can be further extended to design various metamaterials with extreme and specific functionalities.