Linking Microstructures of Wooden Cell Walls to Stiffness and Microstresses of Softwood and Hardwood

  • Hofegger, Jakob (TU Wien)
  • Königsberger, Markus (TU Wien)
  • Pech, Sebastian (TU Wien)
  • Füssl, Josef (TU Wien)

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Geometrical properties of the wooden cell network at the microscale significantly influence the cross-grain mechanical properties of wood [1]. These effects can be effectively studied using finite element (FE) simulations. The key challenge is to obtain realistic microstructure geometries that can suitably be meshed, that accommodate the stochastic variability of the wood cell architecture, and that distinguish between the lignin-rich middle lamella (ML) and the cellulose-dominated cell wall regions, mainly the S2-layer. In this work, a robust computational microstructure generator for softwood and hardwood cell architectures is developed and coupled with FE modeling. First, regular grids of cell centers and potentially cell corners are generated, distorted to account for variability, and then translated to cells. Generation of hardwood cell structures is based on power diagrams [2], an extension of Voronoi tessellation. Based on volume fractions of lumen, vessels, S2 layer, and ML layer, the full microstructure is then built up by Bézier curves, ensuring well-defined interfaces. 2D FE-meshes are finally generated using the open-source software GMSH, see Figure 1(a), and mechanical simulations are performed considering generalized periodic boundary conditions [3] in Ferrite/Julia. The model is then used to establish links between cell microstructure, on the one hand, and elastic wood stiffness or local microstress distributions, on the other hand. The framework quantifies the substantial increase in rolling shear stiffness of softwoods as distortion intensities increase, whereas the rolling shear stiffness of hardwoods decreases. Stress peaks, as depicted in Fig. 1(b), however, increase in both softwood and hardwood upon increasing distortion. Mechanical simulations of pristine and transparent wood highlight the stiffness boost due to polymer infiltration and the substantial reduction of critical stress peaks. References [1] P. Niemz, A. Teischinger, D. Sandberg. Springer Handbook of Wood Science and Technology. Springer Cham, 2023. DOI: 10.1007/978-3-030-81315-4 [2] F. Aurenhammer: Power diagrams: properties, algorithms and applications. SIAM Journal on Computing, 16 (1) (1987): 78–96, DOI:10.1137/0216006 [3] V.-D. Nguyen, E. Béchet, C. Geuzaine, L. Noels, Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation, Computational Materials Science 55 (2012) 390– 406. DOI: 10.1016/j.commatsci.2011.10.017.