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Influence of the cross-linking of the cellulosic fibrillar network on the effective hygro-mechanical behavior of the wood cell wall

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Abstract

This study aims to analyze the influence of the fibrils oscillations and connections on the effective hygro-elastic behavior of the wood cell wall. For that, two different models of microstructure describing the cell wall are introduced: the model 1S, for which the fibrils are allowed to oscillate in one direction like a sine curve, and the model 2S, for which the fibrils oscillate in two directions as a helix. The effective hygro-elastic behavior of the cell wall associated with each of the two models is computed by numerical periodic homogenization. Then, we analyze the effects of the fibers oscillations on the effective behavior by making varying some parameters such as the shape ratio of the unit cell, the fibrils volume fraction, or the elastic contrast between the matrix and the fibrils. It is shown that the fibrils oscillations have a significant effect on some effective moduli of the cell wall, such as the effective shear moduli \({\widetilde{G}}_{12}\) (for both model 1S and 2S) and \({\widetilde{G}}_{13}\), \({\widetilde{G}}_{23}\) (for model 2S only).

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References

  1. Terashima, N., Fukushima, K.: Heterogeneity in formation of lignin—XI: an autoradiographic study of the heterogeneous formation and structure of pine lignin. Wood Sci. Technol. 22, 259–270 (1988)

    Article  Google Scholar 

  2. Harrington, J.J.: Hierarchical Modelling of Softwood Hygro-elastic Properties. University of Canterbury, Christchurch, New Zealand (2002)

    Google Scholar 

  3. Rafsanjani Abbasi, A.: Multiscale poroelastic model—bridging the gap from cellular to macroscopic scale. PhD thesis, ETH Zürich (2013)

  4. Cave, I.: The anisotropic elasticity of the plant cell wall. Wood Sci. Technol. 2, 268–278 (1968)

    Article  Google Scholar 

  5. Salmén, L., de Ruvo, A.: A model for the prediction of fiber elasticity. Wood Fiber Sci. 17(3), 336–350 (1985)

    Google Scholar 

  6. Persson, K.: Micromechanical Modelling of Wood and Fibre Properties (Structural Mechanics). Department of Mechanics and Materials Lund University, Sweden (2000)

    Google Scholar 

  7. Thuvander, F., Kifetew, G., Berglund, L.A.: Modeling of cell wall drying stresses in wood. Wood Sci. Technol. 36(3), 241–254 (2002)

    Article  Google Scholar 

  8. Hofstetter, K., Gamstedt, E.K.: Hierarchical modelling of microstructural effects on mechanical properties of wood. A review COST Action E35 2004–2008: Wood Machining–Micromechanics and Fracture (2009)

  9. Salmén, L.: Micromechanical understanding of the cell-wall structure. C. R. Biol. 327, 873–880 (2004)

    Article  Google Scholar 

  10. Bardage, S., Donaldson, L., Tokoh, C., Daniel, G.: Ultrastructure of the cell wall of unbeaten Norwayspruce pulp fibre surfaces. Nord. Pulp Pap. Res. J. 19(4), 448–452 (2004)

    Article  Google Scholar 

  11. Salmén, L., Stevanic, J.S., Holmqvist, C., Yu, S.: Moisture induced straining of the cellulosic microfibril. Cellulose 28(6), 3347–3357 (2021)

    Article  Google Scholar 

  12. Salmén, L., Burgert, I.: Cell wall features with regard to mechanical performance. A review COST Action E35 2004–2008: Wood Machining–Micromechanics and Fracture (2009)

  13. Boyd, J.D.: An anatomical explanation for visco-elastic and mechano-sorptive creep in wood, and effects of loading rate on strength. In: Baas P (ed) New perspectives in wood anatomy. Forestry sciences, vol 1. Springer, Dordrecht (1982). https://doi.org/10.1007/978-94-017-2418-0_8

    Chapter  Google Scholar 

  14. Gril, J.: Une modélisation du comportement hygro-rhéologique du bois à partir de sa microstructure (Doctoral dissertation, Paris 6) (1988)

  15. Reza, M., Ruokolainen, J., Vourinen, T.: Out-of-plane orientation of cellulose elementary fibrils on spruce tracheid wall based on imaging with high-resolution transmission electron microscopy. Planta 240(3), 565–573 (2014)

    Article  Google Scholar 

  16. Goring, D.A.: Thermal softening of lignin, hemicelluolose and cellulose. Pulp Pap, pp. 517–527 (1963)

  17. Norimoto, M., Gril, J.: Wood bending using microwave heating. J. Microw. Power Electromagn. Energy. 24(4), 203–212 (1989)

    Article  Google Scholar 

  18. Inoue, M., Aoki, T., Egawa, G.: Development of a new teaching material utilizing recovery of compressive set of wood. Wood Res. Tech. Notes 28, 59–71 (1992)

    Google Scholar 

  19. Bornert, M., Bretheau, T., Gilormini, P.: Homogénéisation en mécanique des matériaux, Tome 1: Matériaux aléatoires élastiques et milieux périodiques (pp. 250). Hermes Science (2001)

  20. Tang, R.C., Hsu, N.N.: Analysis of the relationship between microstructure and elastic properties of the cell wall. Wood Fiber Sci. 5(2), 139–151 (1973)

    Google Scholar 

  21. Ruel, K., Barnould, F., Eriksson, E.: Ultrastructural aspects of wood degradation by sporotrichum pulverulentum—observations on spruce wood impregnated with glucose. Holzforschung 38, 61–68 (1984)

    Article  Google Scholar 

  22. Cristian Neagu, R., Kristofer Gamstedt, E., Bardage, S.L., Lindström, M.: Ultrastructural features affecting mechanical properties of wood fibres. Wood Mat. Sci. Eng. 1(3–4), 146–170 (2006)

    Article  Google Scholar 

  23. Nishino, T., Takano, K., Nakamae, K.: Elastic modulus of the crystalline regions of cellulose polymorphs. J. Polym. Sci. Part B Polym. Phys. 33(11), 1647–1651 (1995)

    Article  Google Scholar 

  24. Mark, R.: Cell Wall Mechanics of Tracheids. Yale University Press, New Haven, USA (1967)

    Google Scholar 

  25. Cave, I.D.: Modelling moisture-related mechanical properties of wood part I: properties of the wood constituents. Wood Sci. Technol. 12(1), 75–86 (1978)

    Article  Google Scholar 

  26. Cousins, W.J.: Young’s modulus of hemicellulose as related to moisture content. Wood Sci. Technol. 12(3), 161–167 (1978)

    Article  Google Scholar 

  27. Bodig, J., Jayne, B.: Mechanics of Wood and Wood Composites, Van Nostrand Reinhold. ed, Colección general Biblioteca (1982)

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Authors and Affiliations

  1. Clermont Auvergne INP, Institut Pascal, Université Clermont Auvergne, 63000, Clermont Ferrand, France

    Nhat-Tung Phan, François Auslender, Joseph Gril & Rostand Moutou Pitti

  2. Inrae, Piaf, University Clermont Auvergne, 63000, Clermont Ferrand, France

    Joseph Gril

  3. Cenarest, IRT, BP 14070, Libreville, Gabon

    Rostand Moutou Pitti

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  1. Nhat-Tung Phan
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  2. François Auslender
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  4. Rostand Moutou Pitti
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Correspondence to François Auslender.

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Appendix

Appendix

1.1 Appendix A: components of the tensor of compliance

For an orthotropic elastic behavior, the expressions of the components of the compliance tensor \(\widetilde{{\underline{{\underline {S} }} }}\), as defined by Eq. (9), as functions of the ones of the tensor of elastic moduli \(\widetilde{{\underline{{\underline {C} }} }}\) are given in Table 4.

Table 4 Components of the effective compliance for an orthotropic elastic behavior
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Phan, NT., Auslender, F., Gril, J. et al. Influence of the cross-linking of the cellulosic fibrillar network on the effective hygro-mechanical behavior of the wood cell wall. Acta Mech 233, 4985–5007 (2022). https://doi.org/10.1007/s00707-022-03355-8

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  • DOI: https://doi.org/10.1007/s00707-022-03355-8

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