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The shrinkage of oak predicted from its anatomical pattern: validation of a cognitive model

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This paper deals with the ability of a scientific strategy to compute the shrinkage behaviour of any oak sample, regardless of its origin, density, growth ring, etc. This approach uses the description of the actual oak structure at the annual ring level (i.e. the spatial organisation of the radial ray-cells, fibre, parenchyma areas and large vessels), to evaluate its shrinkage/swelling and elastic properties in the transverse directions. For the shrinkage properties, computed results were compared with experimental values measured on a set of samples depicting a very large diversity of anatomical patterns. The accuracy of our prediction is about 5% in the tangential direction and 20% in the radial direction, which is much better than statistical models over a wide range of variables. These results are discussed and a few microscopic observations with ESEM allow explanation of anomaly points of behaviour to be formulated. Such good results could allow this approach to be used to study the influence of growing conditions or of global changes upon physical wood properties.

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  • Badel E (1999) Détermination des propriétés élastiques et du retrait d’un cerne annuel de chêne dans le plan transverse: description de la morphologie, mesures des propriétés microscopiques et calculs d’homogénéisation. PhD dissertation, ENGREF, Nancy

  • Badel E, Bakour R, Perré P (2006) Investigation of the relationship between anatomical pattern, density and local swelling of oak wood. IAWA 271:55–71

    Google Scholar 

  • Badel E, Perré P (1999) Détermination des propriétés élastiques d’éléments individuels du plan ligneux du chêne par des essais de traction sur micro-éprouvettes. Ann Forest Sci 56:467–478

    Google Scholar 

  • Badel E, Perré P (2001) Using a digital X-ray imaging device to measure the swelling coefficients of a group of wood cells. NDT&E 34:345–353

    Article  CAS  Google Scholar 

  • Badel E, Perré P (2002) Predicting oak wood properties using X-ray inspection: representation, homogenisation and localisation. Part I: Digital X-ray imaging and representation by finite elements. Ann Forest Sci 59:767–776

    Article  Google Scholar 

  • Bakour R (2003) Influence de l’espèce et de la provenance des deux principaux chênes français (Quercus Robur L.; Quercus Petrea Liebl.) sur la structure anatomique et les propriétés du bois de merrain. PhD dissertation, ENGREF, Nancy

  • Barber NF (1968) A theoritical model of shrinking wood. Holzforschung 22:97–103

    Google Scholar 

  • Beismann H, Schweingruber F, Speck T, Korner C (2002) Mechanical properties of spruce and beech wood grown in elevated CO2. Trees -- Struct Funct 168:511–518

    Google Scholar 

  • Berges L, Dupouey J-L, Franc A (2000) Long-term changes in wood density and radial growth of Quercus petraea Liebl. in northern France since the middle of the nineteenth century. Trees -- Struct Funct 147:398–408

    Google Scholar 

  • Burgert I, Bernasconi A, Niklas KJ, Eckstein (2001) The influence of rays on the transverse elastic anisotropy in green wood of deciduous trees. Holzforschung 55:449–454

    Article  CAS  Google Scholar 

  • Clair B, Ruelle J, Thibaut B (2003) Relationship between growth stress, mechanical-physical properties and proportion of fibre with gelatinous layer in chestnut (castanea sativa mill.). Holzforschung 572:189–195

    Article  Google Scholar 

  • El Amri F (1987) Contribution à la modélisation élastique anisotrope du matériau bois-feuillus et résineux. PhD dissertation, I.N.P.L., Nancy

  • Eyono Owoundi R (1992) Modélisation de la rétractibilite du bois en relation avec des paramètres de la structure de l’accroissement annuel et de la position dans l’arbre chez Quercus robur et Q. petraea. PhD dissertation, ENGREF, Nancy

  • Farruggia F (1998) Détermination du comportement élastique d’un ensemble de fibres de bois à partir de son organisation cellulaire et d’essais mécaniques sous microscope. PhD dissertation, ENGREF, Nancy

  • Gu H, Zink-Sharp A, Sell J (2001) Hypothesis on the role of cell wall structure in differential transverse shrinkage of wood. Holz als Roh- und Werkstoff 59:436–442

    Article  Google Scholar 

  • Holmberg S, Persson K, Petersson H (1999) Nonlinear mechanical behaviour and analysis of wood and fibre materials. Comput Struct 724–725:459–480

    Article  Google Scholar 

  • Kawamura Y (1979) Studies on the properties of rays I. Mokuzai Gakkaishi 25:455–460

    Google Scholar 

  • Kawamura Y (1984) Studies on the properties of rays II. Mokuzai Gakkaishi 30:201–206

    Google Scholar 

  • Keller R, Thiercelin F (1975) Influence des gros rayons ligneux sur quelques proprietes du bois de hetre. Ann Forest Sci 32:113–129

    Article  Google Scholar 

  • Koponen S, Toratti T, Kanerva P (1989) Modelling longitudinal elastic and shrinkage properties of wood. Wood Sci Technol 63:55–63

    Article  Google Scholar 

  • Le Moguedec G (2000) Modélisation de propriétés de base du bois et de leur variabilité chez le chêne sessile (Quercus petrea Liebl.). Simulation en vue de l’évaluation d’une ressource forestière. PhD dsissertation, ENGREF, Nancy

  • Pang S (2002) Predicting anisotropic shringkage of softwood. Part 1: theories. Wood Sci Technol 36:75–91

    Article  CAS  Google Scholar 

  • Perré P (2002). Wood as a multi-scale porous medium: observation, experiment, and modelling. In: First international conference of the European Society for wood mechanics (selected and reviewed papers), EPFL, Lausanne, Switzerland, pp 365–384

  • Perré P (2005) Meshpore: A software able to apply image-based meshing techniques to anisotropic and heterogeneous porous media. Dry Technol 239–11:1993–2006

    Article  Google Scholar 

  • Perré P, Badel E (2003) Predicting oak wood properties using X-ray inspection: representation, homogenisation and localisation. Part II: Computation of macroscopic properties and microscopic stress fields. Ann Forest Sci 60:247–257

    Article  Google Scholar 

  • Salmen L (2004) Micromechanical understanding of the cell-wall structure. Comptes Rendus Biologies 3279–10:873–880

    Article  CAS  Google Scholar 

  • Sanchez-Huber J, Sanchez-Palencia E (1992) Introduction aux méthodes asymptotiques et à l’homogénéisation. Masson, Paris

    Google Scholar 

  • Seco JIF-G, Barra MRD (1996) Growth rate as a predictor of density and mechanical quality of sawn timber from fast growing species. Holz als Roh- und Werkstoff 543:171–174

    Article  Google Scholar 

  • Washusen R, Ilic J (2001) Relationship between shrinkage and tension wood from three provenances of Eucalyptus globulus Labill. Holz als Roh- und Werkstoff 59:85–93

    Article  Google Scholar 

  • Watanabe U, Fujita M, Norimoto M (1998) Transverse shrinkage of coniferous wood cells examined using replica method and power spectrum analysis. Holzforshung 52:200–206

    Article  CAS  Google Scholar 

  • Woodcock S (2002) Wood specific gravity and its radial variations: the many ways to make a tree. Trees—Struct Funct 166:437–443

    Google Scholar 

  • Yamamoto H (1999) A model of the anisotropic swelling and shrinking process of wood. Part 1. Wood Sci Technol 33:311–325

    Article  CAS  Google Scholar 

  • Yamamoto H, Sassus F, Ninomiya M, Gril J (2001) A model of anisotropic swelling and shrinking process of wood; Part 2. A simulation of shrinking wood. Wood Sci Technol 35:167–181

    Article  CAS  Google Scholar 

  • Zhang SY, Nepveu GFM (1994) Modelling intratree wood shrinkage in european oak by measuring wood density. Forest Prod J 4410:42–46

    Google Scholar 

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Correspondence to Eric Badel.

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Communicated by M. Zwieniecki

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Badel, E., Perré, P. The shrinkage of oak predicted from its anatomical pattern: validation of a cognitive model. Trees 21, 111–120 (2007).

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