The cell walls in plants are made up of just four basic building blocks: cellulose (the main structural fibre of the plant kingdom) hemicellulose, lignin and pectin. Although the microstructure of plant cell walls varies in different types of plants, broadly speaking, cellulose fibres reinforce a matrix of hemicellulose and either pectin or lignin. The cellular structure of plants varies too, from the largely honeycomb-like cells of wood to the closed-cell, liquid-filled foam-like parenchyma cells of apples and potatoes and to composites of these two cellular structures, as in arborescent palm stems. The arrangement of the four basic building blocks in plant cell walls and the variations in cellular structure give rise to a remarkably wide range of mechanical properties: Young's modulus varies from 0.3 MPa in parenchyma to 30 GPa in the densest palm, while the compressive strength varies from 0.3 MPa in parenchyma to over 300 MPa in dense palm. The moduli and compressive strength of plant materials span this entire range. This study reviews the composition and microstructure of the cell wall as well as the cellular structure in three plant materials (wood, parenchyma and arborescent palm stems) to explain the wide range in mechanical properties in plants as well as their remarkable mechanical efficiency.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2012.0341

The hierarchical structure and mechanics of plant materials

Biomechanics of cellular solids.

The ultimate values for compressive strength, Young's modulus, and toughness of cylindrical specimens of unitary aspect ratios and uniform grain-size distributions were extrapolated for hydroxyapatite (HAP) to 70 MPa, 9.2 GPa, and 0.36 J cm(-3), and for tricalcium phosphate (TCP), to 315 MPa, 21 GPa, and 2.34 J cm(-3). For total volume porosities of 50%, the corresponding values were determined: for HAP, 9.3 MPa, 1.2 GPa, 0.042 J cm(-3), for TCP, 13 MPa, 1.6 GP, 0.077 J cm(-3). Porosities of HAP specimens ranged from 3%-50%; TCP from 10%-70%. Two pore-size distributions were employed. Exponential dependencies of the mechanical properties were found upon porosity (p < 0.0001). No differences in measured mechanical properties, as determined in compression, could be attributed to pore size. The superiority of TCP increases with density and suggests that a larger or more selective pore-size distribution could be effectively employed in TCP biological implants. This work also suggests the dominant role of secondary calcium phosphates in increasing compressive strengths.

Mechanical properties of sintered hydroxyapatite and tricalcium phosphate ceramic.

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa)

Development and experimental validation of a continuum micromechanics model for the elasticity of wood

Timber Bridges: Design, Construction, Inspection, and Maintenance

Paper about the three dimensional deformation of wooden structures. For its prediction the knowledge of the elastic parameter are needed. Explanations are given about the elastic parameters and how they are obtained. Illustrated with charts and sketch drawings.

Prediction of elastic parameters for wood

Layered systems of various materials are used to fabricate beams, plates and shells. The procedures commonly employed to analyze such systems are based on assumption of rigid interconnection between layers. In some widely used systems, however, this assumption is questionable. The basic phenomenon of interlayer slip is considered and a consistent theory for layered beams is developed. The results of experiments with layered wood beams connected with nails, with and without glued ends, are given. Excellent agreement with the general theory is shown. The importance of interlayer slip effect on the deflection of layered beams is demonstrated. The procedures developed can be used for any mechanically-connected beam system.

Layered Beam Systems with Interlayer Slip

The major factors which must be considered in the analysis of layered wood systems, such as wood joist floors, are the orthotropic and variable properties of the wood materials, the incomplete composite action due to interlayer slip, and gaps in sheathing layers at joints between pieces of sheathing. The development of a finite element method for the analysis of layered wood systems, which correctly incorporates all major factors for the first time, is described. Comparisons of measured and computed deflections for T-beams and floors are given and show generally excellent agreement.

Finite Element Analysis of Layered Wood Systems

Results of a large scale study of orthotropic elastic properties of wood are presented. The general theory for elastic behavior of wood is presented for compression loading at general angles to ring and grain. Experimental work, for four species of wood, utilizing a total of 588 specimens is presented. Comparison of theoretical and measured strain is provided and a statistical analysis of the data is developed. Agreement between the theoretical and experimental strain was reasonably good for loading within a principal orthotropic plane; however, large errors seem to exist for general loading out of the principal planes. The study suggests new research efforts are needed to incorporate the nonhomogeneous characteristics of wood in the theory. Refined experimental techniques are also needed to better evaluate the elastic behavior of wood loaded at general angles to the orthotropic axes.

James R. Goodman

Papers

Prediction of elastic parameters for wood

Layered Beam Systems with Interlayer Slip

Finite Element Analysis of Layered Wood Systems

Orthotropic Elastic Properties of Wood

FEAFLO: A program for the analysis of layered wood systems