Predicting of oak wood properties using X-ray inspection: representation, homogenisation and localisation. Part II: Computation of macroscopic properties and microscopic stress fields

Abstract

-This paper is the second part of a comprehensive approach that allows the elastic and shrinkage properties of oak to be determined from the properties of the anatomical tissues and the spatial distribution of those tissues, obtained by a high resolution digital X-ray imaging device. The computation of the macroscopic properties employs a 2-D numerical tool, called MorphoPore, that utilises periodic homogenisation over the representative volume. The paper starts with the derivation of the mechanical formulation and analyses the effect of mesh refinement on the overall solution quality. Thereafter, a first example is presented that depicts the effect of fibre proportion and fibre zone shape on the macroscopic properties using a virtual anatomical pattern and a second example uses finite element meshes built from actual patterns coming from two positions of the same tree, just before and just after thinning the forest stand. The approach presented in this research allows the increase of rigidity and shrinkage coefficients due to the increase of the annual ring width to be quantified. Finally, two localisation problems are proposed in which the micro-stress fields are computed from the macroscopic loading. The first case assumes that no macroscopic stress field exists (free shrinkage configuration), whereas the second assumes that the macroscopic displacement is constrained along one direction (drying configuration).wood / homogenisation / modelling / numerical computation Résumé -Utilisation de l'imagerie X pour la prédiction du bois de chêne : représentation, homogénéisation et localisation. Partie II : Calcul des propriétés macroscopiques et des champs de micro-contraintes. Cet article est la deuxième partie d'une approche complète qui permet de prédire les propriétés élastiques et de retrait du chêne à partir des propriétés des tissus qui le composent et de leur distribution spatiale décrite par un système d'imagerie X de haute résolution spatiale. Le calcul des propriétés macroscopique est effectué par homogénéisation de milieux périodiques sur un volume élémentaire représentatif à partir d'un code numérique 2-D, appelé MorphoPore. Ce papier commence par la présentation de la formulation mécanique. Viennent ensuite quelques considérations sur l'effet du raffinement du maillage numérique. À l'aide de plans ligneux virtuels, le premier exemple d'application montre l'effet de la proportion des fibres et de la forme de zone de fibres sur les propriétés macroscopiques. Le deuxième exemple utilise deux plans ligneux réels, provenant du même arbre. La seconde zone produite juste après éclaircie, a un accroissement annuel très important. Notre approche permet de quantifier l'augmentation des rigidités et des coefficients de retrait. Enfin, deux exemples de localisation sont proposés. Cette démarche permet le calcul des champs de micro-contraintes à partir du chargement macroscopique de la structure. Le premier cas considère l'absence de contrainte macroscopique (retrait libre) tandis que le deuxième considère...

Distribution of structure and lignin within growth rings of Norway spruce

“…Nowadays, various computational approaches exist to calculate material, such as density and permeability (e.g. Perré and Badel 2003), and mechanical properties (Hofstetter et al 2005;Badel and Perré 2007;Qing and Mishnaevsky 2009). Hereby, either mean values for the individual factors are used or small cell structures are digitized from microscopic images (e.g., Derome et al 2011a).…”

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

“…The modelling tool chain has been detailed in previous papers (Badel and Perré 2002;Perré and Badel 2003). The main principles are summarised as follows.…”

“…For several years, we have been presenting the different elements of a complete modelling tool chain. In two previous papers, (Badel and Perré 2002;Perré and Badel 2003), we described a modelling tool that is able to predict the shrinkage/swelling and the elastic properties of oak wood in the transverse directions. This model is based on the description of the actual anatomical structure of the annual ring and takes the microscopic properties of each tissue into account (Badel andPerré 1999, 2001).…”

Multiscale aspects of heat and mass transfer during drying

“…11 and 12, respectively. The detail of the formal expansion in powers of ε for the mechanical problems encountered in drying can be found elsewhere: for elasticity (Sanchez-Palencia 1980;Léné 1984;Sanchez-Hubert and Sanchez-Palencia 1992), for thermo-elasticity (L'Hostis 1996) and for shrinkage (Perré 2002;Perré and Badel 2003).…”

“…(ξ 12 ) corresponds to the shear problem. Solid lines represent the initial contours of tissues (Perré and Badel 2003). Color code, from dark to light : ray cells, fiber zones, parenchyma cells, and vessels This approach allowed us to quantify the effect of fiber proportion and fiber zone shape on the macroscopic values or to predict the increase of rigidity and shrinkage coefficients due to the increase of the annual ring width (Perré and Badel 2003).…”