3D hierarchical computational model of wood as a cellular material with fibril reinforced, heterogeneous multiple layers
Introduction
In recent years, wood has reappeared as a promising building material, what made the problem of prediction of strength and reliability of wooden parts more significant for practical applications. Further, many researchers invested a lot of efforts in the analysis of microstructure-strength relationships of wood, seeking the recipes for optimal design of materials and construction in the framework of the biomimicking concepts (Vincent, 1990, Gordon and Jeronimidis, 1980, Fratzl and Weinkamer, 2007).
Wood is a natural composite material with outstanding mechanical properties, in particular with regard to its low density. At the microlevel, it is a cellular material, built up by tube-shaped cells oriented fairly parallel to the stem direction. Softwood contains regions of latewood, earlywood and transitional regions. In earlywood, cell walls are thinner and the cell cross-sections are larger than in latewood, within each annual ring. The macroscopic properties of softwood are highly dependent on the properties of its constituents as well as the micro- and nanostructure, such as cell dimension and shape, wall thickness and microfibril angles.
The purpose of this work is to develop a multiscale micromechanical model of wood, taking into account its microstructures at several scale levels, and to apply this model to the analysis of the effect of microstructural parameters of wood (microfibril angles/MFAs, the thickness of the cell walls, the shape of the cell cross-section and wood density) on the elastic properties of wood. To solve this problem, the numerical mesomechanical analysis of the deformation behavior of wood was employed (Mishnaevsky, 2005, Mishnaevsky, 2007, Mishnaevsky and Qing, 2008). A 3D hierarchical unit cell model of wood representing a wood cell as a hexagon with multilayered, heterogeneous, fibril-reinforced walls, was developed using the parametric finite element modeling techniques. The input data (elastic properties of the cell wall layers) have been determined with the use of Halpin–Tsai model (Halpin and Kardos, 1976) of cell wall layer as a fibril reinforced composite. The effect of softwood microstructures on its elastic properties and stiffness was studied in the systematic computational experiments. In our later studies, this model will be used to study the microstructural sources of high damage resistance and strength of wood.
Section snippets
Short literature review: 3D micromechanical modeling of softwood
The theoretical and numerous micromechanical models of softwood can be divided into three main groups, which correspond typically to specific scale levels: cellular models, homogenization-based models and composite models.
The cellular models provide the natural framework for the analysis of the mechanical behavior of softwood at the mesoscale. In the framework of cellular models, the wood has been represented as honeycomb with regular hexagons (Easterling et al., 1982), irregular hexagons (
3D mesomechanical FE-model of softwood
The microstructure of softwood at the levels of cell walls/microfibrils can be described as follows. The cell walls of softwood represent as a kind of multilayer material which consists of a primary wall (P) and a secondary wall (S) (Mark, 1967). The primary and secondary walls can be regarded as fiber-reinforced composites, consisting of cellulose, hemicellulose and lignin. The microfibrils are randomly distributed in the primary wall. The secondary wall consists of three layers with different
Stress distribution on interfaces between layers
In the paper, we study the influence of microstructure on the elastic properties of latewood, whose density is 1000 kg/m3 (except for the case of varying density considered in Section 4.5). The thicknesses of layers M, P, S1, S2 and S3 (denoted as TM0, TP0, T10, T20 and T30, respectively) are shown in Table 2. A 3D finite element model of the cells with regular hexagon shape, whose characteristic parameters T(=R) is 7.684 μm, was generated using the above procedure. Data are presented here for
Conclusions
A 3D hierarchical computational model of deformation and stiffness of wood is developed. This model takes into account the structures of wood at several scale levels (cellularity, multilayered nature of cell walls, composite-like structures of layers building the walls). This model allows predicting macroscopic elastic properties and stiffness of timber for a given cellular geometry and assumed distribution of microfibril angles within the cell walls.
With the use of the developed hierarchical
Acknowledgements
The authors gratefully acknowledge the financial support of the Royal Danish Ministry of Foreign Affairs via the Danida project “Development of wind energy technologies in Nepal on the basis of natural materials” (Danida Ref. No. 104. DAN. 8-913).
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