ECCOMAS 2024

Residual stress analysis in wood and its application

  • Muench, Ingo (TU Dortmund)
  • Wulf, Jan Bernd (TU Dortmund)

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We simulate the growth of trees using geometric data from the morphology of real trees and with the help of a phase field model to investigate the development of residual stresses in the wood matrix [1-3]. The residual stress state protects the tree from microstructural buckling of the wood fibres on the bending compression side. While in the residual stress state the young, outer layers of wood are under tensile stress, the older, inner layers of wood exhibit compressive stress. This state changes with each growth period and also adapts to external load changes. If, for example, a tree is subjected to permanent eccentric loading by a technical construction, the natural residual stress state will return to normal after several growth periods. Nevertheless, the disturbance remains to some extent and is particularly noticeable in the deeper layers of wood. This means that the load history influences the residual stress state, which we demonstrate using examples. Our aim is to analyse the load-bearing capacity of trees in relation to the bending stress in more detail in order to better define the permissible load limit, e.g. for technical constructions [4]. An analytical example also shows how residual stresses in wood can be utilised in construction and how this building element can be produced sustainably. REFERENCES [1] J.B. Wulf, I. Muench. Residual Stresses in Green Wood Based on a Phase Field Model. In: Amziane, S., Merta, I., Page, J. (eds) Bio-Based Building Materials. ICBBM 2023. RILEM Bookseries 45: 899-910, Springer, 2023. https://doi.org/10.1007/978-3-031-33465-8_69 [2] J.B. Wulf, I. Muench. Growth of green wood based on a phase field model. Proc. Appl. Math. Mech., 22(1), 1-6, 2022. https://doi.org/10.1002/pamm.202200067 [3] J.B. Wulf, I. Muench. Topology evolution of composite structures based on a phase field model. Proc. Appl. Math. Mech. 20(1), 2021. https://doi.org/10.1002/pamm.202000163 [4] I. Muench, S. Loske. A deterministic model combining NDT to estimate permissible bending loads on trees. ce/papers, 6(5), 258-263, 2023. https://doi.org/10.1002/cepa.2060