Taking a Moment to Characterize the Bending Response of Thin Sheet Materials

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.