Data-Driven Conditional Diffusion Generation Method for Anisotropic Mechanical Metamaterial Unit Cells

Abstract

: Designing two-dimensional anisotropic mechanical metamaterial unit cells from prescribed effective properties remains a challenging inverse problem, particularly when directional stiffness and material usage need to be controlled simultaneously. In this work, a data-driven conditional diffusion framework is developed for generating unit-cell structures with target effective elastic moduli and volume fractions. A structure–property database containing 57,000 binary unit-cell images is first established through a random target-property-driven inverse homogenization method. The effective elastic moduli in the x and y directions, together with the volume fraction, are used as conditional labels, denoted as ( E x , E y , V ). A conditional denoising diffusion probabilistic model (DDPM) with a U-Net denoising backbone, referred to as DDPM-UNet, is then trained to generate unit-cell layouts under prescribed property conditions. To improve the consistency between generated geometries and target properties, a convolutional neural network (CNN) surrogate model is introduced. The CNN provides a property-consistency loss during diffusion model fine-tuning and is also used as a fast evaluator for candidate screening during inference. Compared with DDPM-UNet, the DDPM-UNet-CNN framework produces more valid candidates under 5%, 10%, and 20% relative error thresholds. FEA-based re-homogenization further shows that the selected candidates generally approach the prescribed effective properties. The developed framework provides a practical generative route for identifying candidate anisotropic mechanical metamaterial unit cells under prescribed property conditions.