Micro-Mechanical Modelling and Out-Of-Plane Simulation of Paperboard

  • Görtz, Morgan (Fraunhofer-Chalmers Centre)
  • Kettil, Gustav (Fraunhofer-Chalmers Centre)
  • Mårtensson, Rebecka (Fraunhofer-Chalmers Centre)
  • Borgqvist, Eric (Tetra Pak)
  • Edelvik, Fredrik (Fraunhofer-Chalmers Centre)

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The microstructure of paperboard is composed of several different types of wood fibers connected through mechanical interlocking and microscopic forces. The wood fiber types, fiber orientation, and other microscopic factors directly affect the material's structural properties. Resolving these micro-scale properties in a numerical model leads to high computational complexity, but is required for simulations affected by the fiber structure. In [1], a linear model based on Timoshenko beams was validated by recreating the initial linear tensile stiffness and bending resistance response in both machine-direction and cross-direction. This validation was performed on different 400 g/m$^2$ three-ply paperboard models consisting of both CTMP and kraft pulp. In [1], fibers were placed stochastically, which was sufficient for the properties investigated, but leads to models with out-of-plane compressive stiffness magnitudes lower than expected. This shortcoming has been addressed by developing an efficient geometric algorithm for network generation that constructs models with a densely packed fiber structure. With this improvement, along with improvements in fiber-fiber contact handling, the micro-mechanical model achieves representative out-of-plane stiffness while retaining the previously validated mechanical properties. The validation was performed by comparing elastic responses to experimental data [2] (both in-plane and out-of-plane). In this talk, the network generating process, fiber-fiber contact handling, and the validation results will be presented. [1] Morgan Görtz et al., Iterative method for large-scale Timoshenko beam models, assessed on commercial-grade paperboard, Computational Mechanics, 2024. [2] Eric Borgqvist, Continuum modelling of the mechanical response of paper-based materials, PhD thesis, Lunds University, 2016.