Hygro-elasto-plastic model for planar orthotropic material

Abstract

a b s t r a c tAn in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under local strain differences. A few examples are presented of the effect of the anisotropy and moisture streaks under stretching and drying conditions on strain differences and buckling. The internal stresses were studied through a case in which the drying of different layers occurred at different stages. Both the anisotropy and moisture streaks were capable of rendering the buckling of the sample visible. The permanency of these defects highly depends on several process stages and tension conditions of the sheet, as demonstrated in this paper. The application possibilities of the hygro-elasto-plastic model are diverse, including investigation into several phenomena and defects appearing in drying, converting and printing process conditions.

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

“…The presented elasto-plastic model indicated that permanent waviness/fluting can be generated with elasto-plastic model simulations. Both studied cases presented in this paper, together with earlier studies at [33], proved the usefulness of the model in predicting the challenging deformation phenomena of orthotropic paper sheets.…”

“…(10), the parameters A 1 , A 2 , A 3 and n are the fitting constants, see Table 1. The hygroexpansivity model is based on the measurements and fitting procedures presented in [53] and [33]. The hygroexpansion coefficients β for every in-plane direction are defined by the equation…”

“…Buckling streakiness i.e. bagginess of paper web has been simulated using hygro-elasto-plastic model (LE-model) introduced in [33]. In the LE-model, the in-plane elasto-plastic constitutive material model and hygroexpansivity model as a function of dry solids content (DSC) and the anisotropy index of fiber orientation are applied for numerical solutions of the finite element method.…”

Factors affecting the hygroexpansion of paper

“…Additionally, the hygroexpansion is more affected by drying restraints when the solid content is high [175]. For dry solid contents from 55 to 100%, an increase in hygroexpansion from *0.04 to *0.16 for softwood freely dried pulp was reported [193].…”

“…This was stated as being due to the increased inter-fiber contact (see section ''Inter-fiber contact'') and the effects of pore volume [23,29,105,192,193]. However, the effect of the density is greater in freely dried sheets than in sheets dried under restraint [105].…”