Open Access

ARTICLE

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

Hao Sun, Xiaohong Ding^*, Min Xiong, Heng Zhang

School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, China

* Corresponding Author: Xiaohong Ding. Email:

(This article belongs to the Special Issue: Advanced Computational Modeling and Optimization for Lightweight Materials and Structures)

Computers, Materials & Continua 2026, 89(2), 14 https://doi.org/10.32604/cmc.2026.087308

Received 16 June 2026; Accepted 03 August 2026; Issue published 15 September 2026

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.

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Keywords

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