, Volume 27, Issue 1, pp 321–336 | Cite as

Key parameters controlling stiffness variability within trees: a multiscale experimental–numerical approach

  • Leopold WagnerEmail author
  • Thomas K. Bader
  • David Auty
  • Karin de Borst
Original Paper


Microstructural properties of wood vary considerably within a tree. Knowledge of these properties and a better understanding of their relationship to the macroscopic mechanical performance of wood are crucial to optimize the yield and economic value of forest stocks. This holds particularly for the end-use requirements in engineering applications. In this study the microstructure–stiffness relationships of Scots pine are examined with a focus on the effects of the microstructural variability on the elastic properties of wood at different length scales. For this purpose, we have augmented microstructural data acquired using SilviScan-3™ (namely wood density, cell dimensions, earlywood and latewood proportion, microfibril angle) with local measurements of these quantities and of the chemical composition derived from wide-angle X-ray scattering, light microscopy, and thermogravimetric analysis, respectively. The stiffness properties were determined by means of ultrasonic tests at the clear wood scale and by means of nanoindentation at the cell wall scale. In addition, micro-mechanical modeling was applied to assess the causal relations between structural and mechanical properties and to complement the experimental investigations. Typical variability profiles of microstructural and mechanical properties are shown from pith to bark, across a single growth ring and from earlywood to latewood. The clear increase of the longitudinal stiffness as well as the rather constant transverse stiffness from pith to bark could be explained by the variation in microfibril angle and wood density over the entire radial distance. The dependence of local cell wall stiffness on the local microfibril angle was also demonstrated. However, the local properties did not necessarily follow the trends observed at the macroscopic scale and exhibited only a weak relationship with the macroscopic mechanical properties. While the relationship between silvicultural practice and wood microstructure remains to be modeled using statistical techniques, the influence of microstructural properties on the macroscopic mechanical behavior of wood can now be described by a physical model. The knowledge gained by these investigations and the availability of a new micromechanical model, which allows transferring these findings to non-tested material, will be valuable for wood quality assessment and optimization in timber engineering.


Micromechanics Modeling Scots pine Structure–stiffness relationship Within-tree variability Wood quality 



The authors would like to acknowledge Prof. Herwig Peterlik (University of Vienna) and Dr Thomas Koch (Vienna University of Technology) for providing the equipment for the WAXS and TGA measurements, respectively. The SilviScan-3™ work was undertaken as part of the David Auty’s PhD thesis, which was jointly funded by Corporate and Forestry Services, Forestry Commission, UK, and the Scottish Forestry Trust. Additional funding was provided by the European Cooperation in Science and Technology (COST) program, under the Short Term Scientific Mission initiative under COST Actions E50 and FP0802.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Leopold Wagner
    • 1
    Email author
  • Thomas K. Bader
    • 1
  • David Auty
    • 2
    • 3
  • Karin de Borst
    • 4
  1. 1.Institute for Mechanics of Materials and StructuresVienna University of TechnologyViennaAustria
  2. 2.University of AberdeenAberdeenScotland, UK
  3. 3.Département des sciences du bois et de la forêt, Pavillon Gene-H.-KrugerUniversité LavalQuebecCanada
  4. 4.School of EngineeringUniversity of GlasgowGlasgowScotland, UK

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