Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress–strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.

Mechanical metamaterials have garnered significant attention in materials and mechanics due to their unique geometric designs and tunable properties. However, metamaterials that allow for simultaneous multi-parameter control remain relatively scarce. This study introduces a multifunctional mechanical metamaterial where density, Young’s modulus, Poisson’s ratio, and thermal expansion coefficient are coordinately tunable through a combination of geometric design and material distribution. The influence of geometric and material parameters on the effective properties of the proposed metamaterial was systematically investigated through analytical solution, finite element simulation and experimental measurement. The results demonstrate that adjusting geometric parameters enables the structure to achieve a combination of lightweight characteristics, high adaptability, and negative Poisson’s ratio. Furthermore, the introduction of heterogeneous materials, leveraging the thermal strain mismatch at their interfaces, allows for simultaneous control over the structure’s thermal deformation, enabling either negative or positive thermal expansion. These combined properties are difficult to achieve with existing natural or artificial materials. This work can provide potential applications in flexible devices, smart structures, and thermal management.

Smooth and curved microstructural topologies found in nature—from soap films to trabecular bone—have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far are ad hoc, raising the challenge: how to systematically and efficiently inverse design such artificial microstructures with targeted topological features? Herein, surface curvature is explored as a design modality and a deep learning framework is presented to produce topologies with as-desired curvature profiles. The inverse design framework can generalize to diverse topological features such as tubular, membranous, and particulate features. Moreover, successful generalization beyond both the design and data space is demonstrated by inverse designing topologies that mimic the curvature profile of trabecular bone, spinodoid topologies, and periodic nodal surfaces for application in bio-scaffolds and implants. Lastly, curvature and mechanics are bridged by showing how topological curvature can be designed to promote mechanically beneficial stretching-dominated deformation over bending-dominated deformation.