# Multiscale modelling of delignified wood's thermal and elastic behaviour

Yi Hien Chin, François Auslender, Joseph Gril, Christophe Vial, Rostand Moutou Pitti, Salah-Eddine Ouldboukhitine, Nicolas Labonne, Pascal Biwole

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Yi Hien Chin, François Auslender, Joseph Gril, Christophe Vial, Rostand Moutou Pitti, et al. Multiscale modelling of delignified wood's thermal and elastic behaviour. 13èmes journées du GDR 3544 "Sciences du bois", 20-22 novembre 2024, Nov 2024, Nantes, France. 2024. [hal-05207049](https://hal.science/hal-05207049v1)

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# Multiscale modelling of delignified wood's thermal and elastic behaviour

CHIN Yi Hien¹,², AUSLENDER François¹, GRIL Joseph¹,³, VIAL Christophe¹, MOUTOU PITTI Rostand¹,⁴, OULDBOUKHITINE Salah-Eddine¹, LABONNE Nicolas², BIWOLE Pascal¹,⁵,⁶

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

²Dagard Company, 23600 Boussac, France.

³Université Clermont Auvergne, INRAE, PIAF, 63000 Clermont-Ferrand, France.

⁴CENAREST, IRT, BP 14070, Libreville, Gabon.

⁵MINES Paris, PSL Research University, PERSEE - Center for Processes, Renewable Energies and Energy Systems, France.

⁶California State Polytechnic University, Humboldt, School of Engineering, Arcata, CA 95521, USA.

yi_hien.chin@uca.fr

B58

## Context & Objectives

Delignification involves the extraction of non-cellulosic substances from wood through chemical treatment, transforming wood into a bio-sourced insulating material while preserving its hierarchically aligned cellulosic structures (Fig.1 & Fig.2).

<figure><img src="image_3.png" /><figcaption>Fig.1: Illustration of delignification effect at micro-scale.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig.2: SEM images of poplar wood after delignification treatment compared with native wood.</figcaption></figure>

Due to the lack of in-depth thermal and mechanical study exploring delignified wood to date, this study proposes a **multiscale homogenisation modelling** approach to examine its **thermal conductivity** and **elastic properties**.

## Multiscale homogenisation modelling approach

A representative volume element (RVE) refers to a portion of a material whose effective behaviour represents the material as a whole at the next scale. The input data were derived from the works of Phan et al. [1] and Eitelberger & Hofstetter [2]. The multiscale homogenisation procedure involved RVEs at different length scales:

**Nanoscale:** Self-consistent model of the polymer network consisting of lignin, hemicelluloses and nanopores.

**Microscale:** An RVE of cell wall material made up of cellulose fibrils and a polymer matrix.

**Mesoscale:** An RVE of earlywood with hexagonal cell, where the cell wall layers consist of S1(+ML+P), S2 and S3 with properties rotated at the microfibril angle (MFA). An RVE of earlywood with a vessel. An RVE of latewood.

**Macroscale:** An RVE of the annual growth ring.

The boundary conditions were applied using the built-in periodic condition feature in the Heat Transfer and Structural Mechanics modules of COMSOL Multiphysics® software [3]. The Identical Mesh feature was used in the mesh sequence by ensuring that each pair of matching boundaries share the same mesh. The finite element mesh of each RVE at various scales is shown in Fig. 3.

<figure><img src="image_5.png" /><figcaption>Fig.3: Meshes of different RVEs.</figcaption></figure>

## Results & Discussions

<figure><img src="image_6.png" /><figcaption>Fig.4: Longitudinal, tangential and radial thermal conductivities of hardwood and softwood determined by the annual growth ring RVE model.</figcaption></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Fig.5: The 9 'engineer' macroscopic moduli of native, nanoporous and matrix-free hardwood and softwood.</figcaption></figure>

* After delignification, nanoporosity, microcrack ratio, and wood species influence density, which directly correlates with the thermal and elastic properties of the wood (Fig. 4–6).

<figure><img src="image_9.png" /><figcaption>Fig.6: Density vs. macroscopic thermal and mechanical behaviours of wood.</figcaption></figure>

Delignification

<figure><img src="image_10.png" /></figure>

Porosity

<figure><img src="image_11.png" /></figure>

Density

<figure><img src="image_12.png" /></figure>

Thermal conductivity

<figure><img src="image_13.png" /></figure>

Elastic modulus

## Conclusions & Perspectives

* The homogenization-based multiscale models reliably capture key thermal and elastic trends associated to structural and geometric changes in both native and delignified wood.

* This approach encourages the use of modified wood by effectively managing thermal and mechanical anisotropy, with more pronounced changes in the transverse direction compared to the longitudinal direction.

* Future studies should consider factors such as water content, fibril alignment, cell wall thickness, vessel diameter, and earlywood-latewood ratio, with validations conducted on a larger set of delignified wood samples.

## References

[1] Phan, N.-T., Auslender, F., Gril, J., & Moutou Pitti, R. (2024). Effects of cellulose fibril cross-linking on the mechanical behavior of wood at different scales. Wood Science and Technology, 58(4), 1555–1583.

[2] Eitelberger J, Hofstetter K (2011) Prediction of transport properties of wood below the fiber saturation point – A multiscale homogenization approach and its experimental validation. Composites Science and Technology, 71(2), 134–144.

[3] COMSOL AB (n.d.) COMSOL Multiphysics® v. 6.2 [Computer software]. www.comsol.com

## Acknowledgments

This work is supported by the French National Research Agency (ANR) and the company Dagard, under "France Relance" plan.

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FRANCE
RELANC

ANR

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I-SITE
CLERMONT
Clermont Auvergne Project