Empirical plasticity models applied for paper sheets having different anisotropy and dry solids content levels

A model for moisture-induced dimensional instability in printing paper

“…Experimental results also show a moisture-dependence of the Young's modulus and hardening modulus (Erkkilä et al 2013). Both moduli decrease with increasing moisture content.…”

“…For a kinematic hardening yield criterion, the value of the yield stress determines the radius of the yield surface, whereas the product ( ) determines the location of its center. Although in the literature (Erkkilä et al 2013) more sophisticated hardening laws are presented, it will be assumed for simplicity that a linear kinematic hardening law is sufficient for capturing the major trends in deformation caused by moisture influences. A linear relation between yield stress and moisture content is chosen:…”

“…The history dependent dimensional stability of paper has been studied through hygro-visco-elastic models presented (Roylance et al 1980;Uesaka et al 1989;Lif et al 2005;Lif 2006). In some studies (Lipponen et al 2008;Erkkilä et al 2013;Erkkilä et al 2015), out-of-plane deformations are simulated through elasto-plastic material models with moisture-dependent material properties. These descriptions, however, are not focused on modeling the release of dried-in strains upon wetting, despite the fact that these strains may play a relevant role in the moisture induced deformation.…”

The Curl and Fluting of Paper: The Effect of Elasto-Plasticity

“…In Eq. (8), σ and ε are the stress and strain, respectively; the dry solids content R sc = [0, 1] and the anisotropy index φ dependent fitting parameters are the elastic modulus E, the yield strain ε y and the hardening constant H. The anisotropy index φ is defined as [52] …”

“…where ξ is the fiber orientation anisotropy and γ is the angle from the minor axis of the fiber orientation distribution [52]. The material model was constructed by fitting the equation [33] …”