Fig. 7: Validation of empirical and derived models for crease length evolution with measurement.

a Predicted change in total crease length δℓ_empir. given by Eq. (12) plotted against the measured change in crease length between two successive crumples, \(\delta {\ell }_{\text{meas.}}\equiv {\ell }_{\text{meas.}\,}^{(n)}-{\ell }_{\,\text{meas.}\,}^{(n-1)}\). Open markers correspond to manually segmented data consistent with prior results presented in this work, while filled circles correspond to data which was processed using the automated segmentation as detailed in the Supplementary Methods. A 1:1 reference line (dashed) is provided as a guide to the eye. b The total crease length ℓ_empir. given by Eq. (11) plotted against the measured total crease length ℓ_meas.. c The change in total crease length δℓ_model as predicted by Eq. (20), and d the total crease length \({\ell }_{\,\text{model}\,}^{(n)}\) obtained from Eqs. (14) and (21), against their corresponding measured values, in direct comparison to a and b. Marker colors in all panels correspond to different values of \(\tilde{{{\Delta }}}\), as indicated by the colorbar. We see that both the empirical and derived relations for δℓ and ℓ serve as strong models of measured data, and affirm the suitability of a logarithmic relationship to describe damage evolution in this system.