Abstract
Tissue is a low-density paper product distinguished by a microscale crepe structure. We investigate the relationship between the macroscale tissue tensile response and crepe structure. We propose a parameter called the Crepe Index (CI) that can be measured from edge images of the creped sheet. Crepe Index correlates very well with the measured tensile failure strain (“stretch”), but its correlation with the measured initial elastic stiffness is unclear. A discrete elastoplastic model (DEM) is developed to explain the experimental results and understand the nonlinearity in the tensile curve. The model accounts for both material nonlinearity through a bilinear elastoplastic constitutive law for the sheet material, and the geometric nonlinearity arising from large deformations. The creped sheet is idealized as a triangular wave of prescribed wavelength and waveheight, with nonlinear bending and stretching effects. The model results show that the tensile response is governed by both the nonlinearity of the sheet material (fibre network) and crepe structure (geometry). The yielding in stretching and bending gives rise to an inflection in the tensile response. It is found that the initial stiffness depends not only on CI, but also on parameters such as sheet thickness to crepe-wavelength ratio, and stiffness of sheet material after creping. Thus, the variability in above parameters can be one of the reason for unclear correlation between measured initial stiffness and CI. For CI range of tested commercial tissues, both experiments and model show that stretch varies linearly with CI, with an almost unity slope and a positive intercept (i.e, stretch> CI). Thus, the overall stretch of creped tissue is a sum of CI and network stretching.
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