Wood Science and Technology

, Volume 44, Issue 3, pp 389–398 | Cite as

Knots in trees: strain distribution in a naturally optimised structure

  • Christoph Buksnowitz
  • Christoph Hackspiel
  • Karin Hofstetter
  • Ulrich Müller
  • Wolfgang Gindl
  • Alfred Teischinger
  • Johannes Konnerth


Electronic speckle pattern interferometry was applied to directly measure the distribution of longitudinal, tangential, and shear strains in small boards of Norway spruce (Picea abies (L.) Karst.) exposed to tensile load in longitudinal direction. A sample with a central intergrown knot and one with an equivalent loose knot were compared with reference samples made of clear wood with an artificial central circular or square hole, respectively. The observed measurements were compared with a finite element (FE) simulation. The FE model was based on a geometric model to quantify the local fibre orientation and a micromechanical model to estimate elastic constants of clear wood and knot tissue. Both the measurements and simulation clearly illustrate a rather homogenous strain distribution around the intergrown knot. In comparison, the natural optimisation of dispersing strain peaks is less efficient in the case of loose knots. The artificial circular and square holes in samples with parallel fibre orientation lead to high gradients in the strain field and peak values in vicinity of the disturbance.


Shear Strain Strain Distribution Parallel Fibre Electronic Speckle Pattern Interferometry Clear Wood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Dantec—Ettemeyer (2001) ISTRA for windows, version 3.3.12. Dantec Ettemeyer GmbH, UlmGoogle Scholar
  2. Dumail JF, Kenneth O, Salmén L (2000) An analysis of rolling shear of spruce wood by the iosipescu method. Holzforschung 54:420–426CrossRefGoogle Scholar
  3. Eberhardsteiner J (1995) Biaxial testing of orthotropic materials using electronic speckle pattern interferometry. Measurement 16:139–148CrossRefGoogle Scholar
  4. Eberhardsteiner J (2002) Mechanisches Verhalten von Fichtenholz—Experimentelle Bestimmung der biaxialen Festigkeitseigenschaften. Springer Wien, New YorkGoogle Scholar
  5. Foley C (2001) A three-dimensional paradigm of fiber orientation in timber. Wood Sci Technol 35:453–465CrossRefGoogle Scholar
  6. Gindl W, Sretenovic A, Vincenti A, Müller U (2005) Direct measurement of strain distribution along a wood bond line—part II: effects of adhesive penetration on strain distribution. Holzforschung 59:307–310CrossRefGoogle Scholar
  7. Gingerl M (1998) Realisierung eines optischen Deformationsmesystems zur experi-mentellen Untersuchung des orthotropen Materialverhaltens von Holz bei biaxialer Beanspruchung. Doctoral thesis, Vienna University of TechnologyGoogle Scholar
  8. Hofstetter K, Hellmich C, Eberhardsteiner J (2005) Development and experimental validation of a continuum micromechanics model for the elasticity of wood. Eur J Mech A Solids 24:1030–1053CrossRefGoogle Scholar
  9. Hofstetter K, Hellmich C, Eberhardsteiner J (2007) Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials. A review and an improved approach. Holzforschung 61:343–351CrossRefGoogle Scholar
  10. Jernkvist LO, Thuvander F (2001) Experimental determination of stiffness variation across growth rings in Picea abies. Holzforschung 55:309–317CrossRefGoogle Scholar
  11. Konnerth J, Valla A, Gindl W, Müller U (2006) Measurement of strain distribution in timber finder joints. Wood Sci Technol 40:631–636CrossRefGoogle Scholar
  12. Mattheck C (1991) Trees—the mechanical design. Springer, BerlinGoogle Scholar
  13. Mattheck C (1998) Design in nature—learning from trees. Springer, BerlinGoogle Scholar
  14. Mattheck C, Kubler H (1997) Wood—the internal optimization of trees. Springer, BerlinGoogle Scholar
  15. Mohan NK, Rastogi P (2003) Recent developments in digital speckle pattern interferometry. Opt Lasers Eng 40(5–6):439–445CrossRefGoogle Scholar
  16. Müller U, Sretenovic A, Vincenti A, Gindl W (2005) Direct measurement of strain distribution along a wood bond line—part I: shear strain concentration in a lap joint specimen by means of electronic speckle pattern interferometry. Holzforschung 59:300–306CrossRefGoogle Scholar
  17. Müller U, Gindl W, Jeronimidis G (2006) Biomechanics of a branch—stem junction in softwood. Trees Struct Funct 20(5):643–648Google Scholar
  18. Phillips GE, Bodig J, Goodman JR (1981) Flow-grain analogy. Wood Sci 14(2):55–64Google Scholar
  19. Rastogi PK (2001) Measurement of static surface displacements, derivatives of displacements, and three-dimensional surface shapes—examples of applications to non-destructive testing. In: Rastogi PK (ed) Digital speckle pattern interferometry and related techniques. Wiley, New York, pp 141–224Google Scholar
  20. Resch E, Kaliske M (2005) Bestimmung des Faserverlaufs bei Fichtenholz. Leipz Annu Civ Eng Rep 10:117–130Google Scholar
  21. Reuschel JD (1999) Untersuchungen der Faseranordnung natürlicher Faserverbunde und Übertragung der Ergebnisse auf technische Bauteile mit Hilfe der Finite-Elemente-Methode. Dissertation, Forschungszentrum Karlsruhe GmbH, KarlsruheGoogle Scholar
  22. Shigo AL (1985) How tree branches are attached to trunks. Can J Bot 63:1391–1401CrossRefGoogle Scholar
  23. Shigo AL (1990) A new tree biology. Thalacker, BraunschweigGoogle Scholar
  24. Siebert T, El-Ratal W, Wegner R, Ettemeyer A (2002) Combine simulation and experiment in automotive testing with ESPI measurement. Exp Tech 26(3):42–47CrossRefGoogle Scholar
  25. Timell TE (1986) Compression wood in gymnosperms. Springer, BerlinGoogle Scholar
  26. Trendelenburg R (1955) Das Holz als Rohstoff. Carl Hanser Verlag, MünchenGoogle Scholar
  27. Ullmann E (2004) Ullmann’s encyclopedia of industrial chemistry, 7th edn. Wiley-VCH, New YorkGoogle Scholar
  28. Valla A, Konnerth J, Keunecke D, Niemz P, Müller U, Gindl W (2010) Comparison of two optical methods for contactless, full field and highly sensitive in plane deformation measurements using the example of plywood (Submitted)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Christoph Buksnowitz
    • 1
  • Christoph Hackspiel
    • 3
  • Karin Hofstetter
    • 3
  • Ulrich Müller
    • 2
  • Wolfgang Gindl
    • 1
  • Alfred Teischinger
    • 1
  • Johannes Konnerth
    • 1
  1. 1.Department of Material Sciences and Process Engineering, Institute of Wood Science and TechnologyUniversity of Natural Resources and Applied Life SciencesViennaAustria
  2. 2.Kompetenzzentrum Holz GmbHLinzAustria
  3. 3.Institute for Mechanics of Materials and StructuresVienna University of TechnologyViennaAustria

Personalised recommendations