Modular metamaterials with deep learning–enabled customizable stress–strain responses

Modular mechanical metamaterials offer unique opportunities for programmable and reconfigurable functionality through simple geometric rearrangements. Inspired by the modularity of Lego blocks, we propose a new class of modular metamaterials composed of three standardized modules—linear, yielding-like, and snap-through buckling elements—that can be assembled into two- and three-dimensional grids to realize diverse nonlinear stress–strain responses. To accelerate design and optimization, we integrate deep learning (DL) with the metamaterial design process. A convolutional neural network-based predictor rapidly estimates the stress–strain curves of given modular configurations, achieving a prediction accuracy of R2>0.999. Furthermore, a conditional variational autoencoder-based inverse designer enables the automatic generation of modular configurations that match target stress–strain curves, demonstrating high fidelity (R2≈0.97). The proposed DL framework allows rapid, scalable, and reprogrammable design of nonlinear mechanical responses without exhaustive simulations or manual tuning. This study establishes a universal, data-driven strategy for the inverse design of modular metamaterials, paving the way toward intelligent, reconfigurable material systems for applications in soft robotics and adaptive structures.