Paper curl modeling

A computational approach for characterization of curl of paper under humidity changes is presented. Asymmetric papers with nonuniform through-thickness fiber orientation distribution are considered. Testing of the constituent layers of the papers considered was conducted at various constant relative humidities to obtain the mechanical properties, moisture content, moisture expansion coefficients and stress relaxation curves. Experiments were performed on asymmetric two-ply laboratory made papers to determine the curl response under moisture loading. The influence of viscoelastic stress relaxation on the curl response was first investigated. Geometrically nonlinear finite element analysis was conducted. It was found that the curvatures relax at an increasing rate with increasing humidities because of moisture enhanced viscoelastic dominance. Computed time-dependent curvatures were compared to experimental measurements which verified the mode shape and time-dependent relaxation response. Geometrically nonlinear finite element analysis revealed that initial deflections may strongly influence the subsequent curl behavior. A sheet with initial curvatures may undergo a bifurcation transition (buckling curl response) if the curvatures strongly interact. After the bifurcation transition, the sheet may or may not assume an unexpected shape. Experiments showed sensitivity of the response to the directions of the initial curvatures, and there are indications of a bifurcation as a result of curvature interaction. A two-ply laminate model was used to analyze curvatures of various asymmetric papers. Differences in fiber orientation distribution and principal fiber orientation angle between the two plies were considered. The analysis showed that the sheet typically bifurcated into a cylindrical and/or twisted shape. A sheet with known through-thickness fiber orientation demonstrated a complex curl response that could be simulated using the approach presented, given that the initial curl shape is known.