Abstract Structured sheet materials such as 3D‐printed rod networks, multi‐material thin shells, and multi‐layer laminates exhibit diverse mechanical behaviors. To avoid the computational burden of native‐scale simulations, data‐driven homogenization offers a promising alternative. This process involves probing a representative patch of material—a unit cell—with a set of stretching and bending tests subject to periodic boundary conditions. Because macro‐scale bending moments are not directly available from native‐scale simulations, existing methods exclusively rely on elastic energy data. Unfortunately, using only elastic energy from uniaxial tests is not sufficient for capturing the full moment‐curvature relationship, and imposing biaxial curvature states would necessarily break periodicity. We present a moment‐based homogenization method that infers curvature coupling using only uniaxial bending tests. Our method computes macro‐scale bending moments from native‐scale simulations for a wide range of mechanical models. To this end, we translate internal deformations into elastic stresses and then integrate these stresses through the thickness and across the unit‐cell patch. We use the resulting homogenized bending moments along with energy data to fit neural bending energy density functions. We demonstrate our method on a diverse set of materials, including multi‐material shells, rod networks, and multi‐layer sheets. Our results show improved accuracy compared to existing approaches and realistic double‐curvature behavior when applied to larger samples.

We revisit the computation of 3D generalized winding numbers, a useful measure for inside-outside classification on triangle meshes with gaps, self-intersections, and open boundaries. At the core of our new method is an analytical reduction of the surface integral that defines the winding number, resulting in a single ray-mesh intersection test and an elementary sum over boundary edges per evaluation. This construction is orders of magnitude more efficient than the state of the art in practice, which we show in an extensive performance benchmark. Conveniently, the method also reduces to the best-available asymptotic complexity in the worst case, and it introduces no approximations apart from floating-point errors. Our algorithm is conceptually simple to understand, straightforward to implement and debug, and it works reliably even on extremely noisy and corrupt input geometry.