Abstract
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.
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References
Dantec—Ettemeyer (2001) ISTRA for windows, version 3.3.12. Dantec Ettemeyer GmbH, Ulm
Dumail JF, Kenneth O, Salmén L (2000) An analysis of rolling shear of spruce wood by the iosipescu method. Holzforschung 54:420–426
Eberhardsteiner J (1995) Biaxial testing of orthotropic materials using electronic speckle pattern interferometry. Measurement 16:139–148
Eberhardsteiner J (2002) Mechanisches Verhalten von Fichtenholz—Experimentelle Bestimmung der biaxialen Festigkeitseigenschaften. Springer Wien, New York
Foley C (2001) A three-dimensional paradigm of fiber orientation in timber. Wood Sci Technol 35:453–465
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 59:307–310
Gingerl M (1998) Realisierung eines optischen Deformationsmesystems zur experi-mentellen Untersuchung des orthotropen Materialverhaltens von Holz bei biaxialer Beanspruchung. Doctoral thesis, Vienna University of Technology
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 24:1030–1053
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 61:343–351
Jernkvist LO, Thuvander F (2001) Experimental determination of stiffness variation across growth rings in Picea abies. Holzforschung 55:309–317
Konnerth J, Valla A, Gindl W, Müller U (2006) Measurement of strain distribution in timber finder joints. Wood Sci Technol 40:631–636
Mattheck C (1991) Trees—the mechanical design. Springer, Berlin
Mattheck C (1998) Design in nature—learning from trees. Springer, Berlin
Mattheck C, Kubler H (1997) Wood—the internal optimization of trees. Springer, Berlin
Mohan NK, Rastogi P (2003) Recent developments in digital speckle pattern interferometry. Opt Lasers Eng 40(5–6):439–445
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 59:300–306
Müller U, Gindl W, Jeronimidis G (2006) Biomechanics of a branch—stem junction in softwood. Trees Struct Funct 20(5):643–648
Phillips GE, Bodig J, Goodman JR (1981) Flow-grain analogy. Wood Sci 14(2):55–64
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 141–224
Resch E, Kaliske M (2005) Bestimmung des Faserverlaufs bei Fichtenholz. Leipz Annu Civ Eng Rep 10:117–130
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, Karlsruhe
Shigo AL (1985) How tree branches are attached to trunks. Can J Bot 63:1391–1401
Shigo AL (1990) A new tree biology. Thalacker, Braunschweig
Siebert T, El-Ratal W, Wegner R, Ettemeyer A (2002) Combine simulation and experiment in automotive testing with ESPI measurement. Exp Tech 26(3):42–47
Timell TE (1986) Compression wood in gymnosperms. Springer, Berlin
Trendelenburg R (1955) Das Holz als Rohstoff. Carl Hanser Verlag, München
Ullmann E (2004) Ullmann’s encyclopedia of industrial chemistry, 7th edn. Wiley-VCH, New York
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)
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This article is dedicated to Gerd Wegener on the occasion of his retirement as professor at the Technische Universität München.
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Buksnowitz, C., Hackspiel, C., Hofstetter, K. et al. Knots in trees: strain distribution in a naturally optimised structure. Wood Sci Technol 44, 389–398 (2010). https://doi.org/10.1007/s00226-010-0352-4
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DOI: https://doi.org/10.1007/s00226-010-0352-4