Generative inverse design of metamaterials with customized stress-strain response

This study presents an inverse design framework that integrates a multi-task variational autoencoder (VAE) with a residual predictor to achieve simultaneous structural reconstruction and mechanical response prediction of lattice-based metamaterials. In this framework, a 28-dimensional binary structural vector and its corresponding stress-strain curve are embedded into a shared latent space, enabling a bidirectional mapping between geometry and mechanical performance. A comprehensive database of over 20,000 three-dimensional lattice topologies, generated through finite element (FE) simulations under quasi-static compression, was used for model training and validation. The residual predictor enhances the stability and accuracy of the VAE in capturing nonlinear features. Under both small-sample and full-sample training regimes, the model demonstrates robust generalization and accurate curve reconstruction, with mean relative area errors (RAE) of 0.08 and 0.0036, respectively. Furthermore, inverse design experiments verify the capability of the framework to generate lattice structures tailored to customized stress-strain responses, including multi-peak, plateau, and oscillatory curves. Compared with conventional strategies, this framework provides a unified, data-driven pathway for on-demand metamaterial design, offering new opportunities for the intelligent and customizable development of architected materials in engineering applications.