Wood and wood products - linking multiscale analysis and structural numerical simulations

Wood is one of the oldest construction materials known to man. Over thousands of years it has been mainly used in a craft framework, so that current design rules are often based on experience and tradition. The scientific knowledge about the material behavior is often surprisingly poor. In order to exploit the extraordinary ecological potential of the material and to enable its structural use also in an industrial framework, improved material models are required. Modern timber construction is characterized by increasing demand of two- and three dimensional bearing components. Dimensioning and design of such sophisticated structures require powerful material models for numerical simulation tools such as the finite element (FE) method. Moreover, the large variability of the macroscopic material properties has to be understood and suitably described to prevent exaggerated safety factors resulting in an uneconomic over-dimensioning of timber members. In order to understand the variability of macroscopic properties of solid wood and the underlying phenomena and to suitably describe them in material models, the hierarchical microstructure of the material has to be considered. At sufficiently small length scales universal constituents common to all wood species and samples as well as universal building principles can be identified. Namely, lignin, hemicellulose, cellulose, and water are such tissue-independent universal constituents with common mechanical properties across the diverse wood species at the molecular level. They build up cell walls resembling fiber-reinforced composites, which are arranged according to a honeycomb pattern. A mathematical formulation of the univeral building principles results in a multiscale micromechanical model for wood which links microstructural characteristics of individual wood samples to macroscopic mechanical characteristics of these samples. Homogenization techniques are employed for this purpose. In particular, the composite structure of the wood cell wall motivates application of continuum micromechanics for estimation of its elastic properties. At the cellular scale, plate-type bending and shear deformations dominate the mechanical behavior, which are more suitably represented by a unit cell approach. Formulation of the localization problem corresponding to the multiscale homogenization scheme allows determination of strain estimates at smaller length scales for given macroscopic loading. Quadratic strain averages (so-called ‘second-order estimates’) over microstructural components turned out to suitably characterize strain peaks in these components. Combination of estimates for such averages with microscale failure criteria delivers predictions for macroscopic elastic limit states. As for solid wood, experimental investigations indicate that wood failure is initiated by shear failure of lignin in the wood cell wall. This can be suitably described mathematically by means of a von Mises- failure criterion. The multiscale models for wood stiffness and elastic limit states are validated by comparison of model predictions for stiffness and strength properties with corresponding experimental results across a multitude of different wood species and different samples. The small errors of the model predictions underline the predictive capabilities of the micromechanical model. For example, the mean prediction errors for the elastic moduli and the shear moduli related to the three principal material directions L, R, and T are each below 10 %. The capability of micromechanical approaches to link macroscopic properties to microstructural characteristics renders such approaches also very appealing for wood products. In this paper, models for a representative of strand-based products, namely the Veneer Strand Board (VSB), as well as for a representative of solid wood-based products, namely the DendroLight panel, are shown. VSB consists of large-area, flat and slender strands with uniform strand shape and dimensions and is typically built up of several layers with different strand orientations. The high-quality strand material results in increased stiffness and strength of the board compared to conventional strand and veneer- based panels. The multiscale model for VSB spans three scales of observations: the strand material, a homogeneous board layer, and the multi-layer board. Continuum micromechanics is applied first in order to estimate the elastic properties of a homogeneous board layer from the stiffness of the strands, their shapes, and their orientations. In the second step, effective stiffness properties of a multi-layer panel are determined by means of classical lamination theory. Thereby, the stacking sequence, the orientation of the principal material directions of the single layers, and the density variation across the board thickness are taken into account. Model validation is again based on independent experiments. Results of tests on specially produced homogeneous boards as well as inhomogeneous boards with a well defined vertical density distribution show a good agreement with corresponding model predictions. This underlines the capability of the model for estimation of the stiffness of strand-based engineered wood products from microstructural features and renders it a powerful tool for parameter studies and product optimization. DendroLight is a three-layered lightweight panel consisting of thin outer layers of solid wood or particle board and a middle layer made up of small cells with webs inclined by an angle of 45° facing alternatively upwards and downwards. The periodic microstructure motivates application of the unit cell method for prediction of the mechanical behavior of this panel. As for plane periodic media, macroscopic unit curvature states are considered as loadings of the unit cell in addition to macroscopic unit strain states. In particular, effective in-plane stiffnesses and bending stiffnesses are obtained. For the purpose of model validation, several panel samples were produced by hand and tested in tension. The experimental results show a good agreement with corresponding stiffness predictions by the model. The multiscale model has already been successfully employed for product characterization and further product development. Since wood is a naturally grown material, it shows growth irregularities, primarily knots and site-related defects. Knots result in a pronounced reduction of stiffness and strength of wooden boards. Due to the highly anisotropic material behavior of wood, the influence of the grain orientation on the mechanical properties of a board is very pronounced and results in high variability in strength and stiffness of structural timber. The latter is a major difficulty in solid wood utilization and brings about the need for wood grading. This motivates investigation of the effects of knots on the mechanical behavior of boards by means of physically-based numerical simulations. In particular, the FE method is combined with sophisticated models for the fiber course and the material behavior. For the description of the local fiber course around a knot, a mathematical algorithm based on a fluid flow approach and polynomial functions fitted to the annual ring course is employed. The algorithm is evaluated at every integration point of the FE model and yields the local three-dimensional fiber orientation there. With respect to the mechanical material behavior, the previously described micromechanical model for solid wood is used, enabling consideration of local variations of microfibril angles or chemical composition of the wood tissue in the vicinity of knots. First results obtained with the numerical simulation tool indicate its capability to estimate the stiffness and strength reduction of wood boards in consequence of knots. On the whole, micromechanical models provide accurate estimates for the mechanical properties of wood and wood products in a fully three-dimensional and orthotropic framework. Also various couplings, e.g. between moisture transport and mechanical behavior, are suitably captured by these models. This makes these models highly valuable for structural simulations, whose predictive and also descriptive capabilities are often limited by the lack of suitable input data or the poor accuracy of available data. Hence, micromechanical modeling activities are expected to support structural analyses of wood structures, but also optimization of processes in wood drying technology.