One-click bending stiffness: Robust and reliable automatic calculation of moment–curvature relation in a cantilever bending test

The cantilever bending test is one of the simplest and most widely used methods to estimate the bending stiffness of textile materials. A nonlinear moment–curvature relationship can be computed from a single image of a cantilevered textile specimen. However, the calculation of curvature involves second-order differentiation of noisy data, which leads to noise amplification. Traditionally, this is handled by subjectively choosing one of many functions to fit the data or by manual tuning of fitting parameters. The user choices ultimately lead to uncertainties in the data fit. This paper presents a novel automatic data processing method for the cantilever test using smoothing splines with automatic parameter selection through cross-validation. The method is verified on a simulated deflection curve with known bending stiffness and then used to characterise real textile specimens. Finally, the method is validated by simulating the deflection curve using the computed stiffness. This method makes it possible, for the first time, to accurately predict the textile curvature even in the presence of severe noise, without needing user inputs prone to human error. The code used for this paper is freely available with sample data on the repository at https://doi.org/10.5281/zenodo.7376939.