Micromechanical network model for the evaluation of quality controls of paper

H. Andrä, F. Edelvik, M. Fredlund, E. Glatt, M. Kabel, R. Lai, A. Mark, L. Martinsson, U. Nyman, S. Rief, Progress in Paper Physics Seminar, Graz, Austria, September 2011, pp. 49-55.


In this paper, we discuss the challenges in modelling and simulating infinitesimal and large deformations of cellulose fiber networks, mainly in the context of the prediction of quality controls for paper. Understanding the influence and sensitivity of macroscopic production parameters like grammage and thickness of paperboard and understanding the influence of the fiber suspension on the quality of paper is important for the development of better papers and for preserving raw materials and energy. The new simulation framework consists of the virtual stochastic paper structure generator PaperGeo, that was integrated in the GeoDict 1 software suite, and the finite element solver FeelMath (Finite Elements for Elastic Materials and Homogenization) for solving the equations of elasticity. The fibers and the contacts are modelled by using geometrically exact beams of Simo-type. The microstructural model and the fiber network model are validated against standard measurements of existing papers in the following way: At first we perform tensile and bending tests to measure the macroscopic stress-strain relations. In the next step we apply a representative macroscopic stress or strain onto the boundaries of realizations of the stochastic fiber network model and compute by homogenization the effective (stiffness) coefficients. Finally we compare the numerical results with the measurements. This procedure can also be used for an identification of elastic parameters on the microscale and to study the sensitivity of the effective (macroscopic) stiffness with regard to the parameters of the microstructure


Authors and Affiliations

  • H. Andrä, Fraunhofer Institute for industrial Mathematics ITWM
  • F. Edelvik, Fraunhofer-Chalmers Centre
  • M. Fredlund, Stora Enso
  • E. Glatt, Fraunhofer Institute for industrial Mathematics ITWM
  • M. Kabel, Fraunhofer Institute for industrial Mathematics ITWM
  • R. Lai, Akzo Nobel
  • A. Mark, Fraunhofer-Chalmers Centre
  • L. Martinsson
  • U. Nyman, Tetra Pak Packaging Solutions AB
  • S. Rief, Fraunhofer Institute for Industrial Mathematics ITWM

Photo credits: Nic McPhee