Geometric quantification for nonlinear deformation in knitted fabrics

Knitted fabrics exemplify a broad class of architected materials capable of large deformations, enabling shape morphing, mechanical biocompatibility, and embedded multifunctionality without material damage. Although geometric nonlinearity has been intuitively utilized in their design, a quantitative description of stitch-resolved deformation and its temporal evolution remains lacking. Here, we introduce a geometric quantification framework that reconstructs smooth yarn centerlines and fabric surfaces from sparse yarn-level representations and extracts interpretable descriptors across dimensions. Applied to representative knitted structures, this framework resolves how global deformation is distributed among stitch reorientation, loop bending, surface bending, and dilation. Moreover, it reveals how regions of large geometric variation emerge, persist, and redistribute over time. Rather than directly measuring stress, these geometric descriptors define a unified geometric state space for comparing knitted structures and identifying candidate regions of mechanical localization. The framework provides a quantitative language for nonlinear deformation in knits and establishes a geometry-based representation that can be coupled to constitutive models, experimental measurements, and graph-based inverse-design workflows.