Modelling and simulation of the nonlinear behaviour of paper: A cellular materials approach

Paper is a stochastic network of fibres, water and additives, and in that sense it may be envisaged as a composite material. Since fibres are much longer than the thickness of the paper sheet, the network is planar and almost two-dimensional. The two-dimensional structure governs many paper properties but the three-dimensional porous structure is also important. Insight into the structural changes that take place when paper is compressed in the paper machine may be gained by modelling and simulation of its viscoelastoplastic behaviour. The present work describes a mathematical model based on the cellular solids theory, characterising the nonlinear rheologic behaviour of the material. This approach results in an unsteady state problem and the resulting set of ODEs is solved by means of the DLSODES subroutine, which uses an integrator based in the Gear method. Experiments were conducted on a laboratory-scale dynamic press in order to validate the mechanical model.