Abstract
Numerical modeling is an efficient tool for experimental validation and for gaining a deeper understanding of complex material phenomena, especially when causal relationships are overlaid by material variability. Wood is such a highly orthotropic and complex material, which in engineering problems however is considered as macro-homogeneous. The aim of this study is to numerically investigate stress and strain states of wood in the radial-tangential plane and the influence of the orthotropic material behavior on the structural response. Model validation is based on experiments performed on clear wood of Norway spruce (Picea abies) by using a biaxial test setup. Three material models were used, namely Hill’s plasticity model, the Hoffman criterion and a novel quadratic multi-surface (QMS) criterion. After validation on the local material scale, the models were applied to the engineering problem of compression perpendicular to the grain for studying the effect of the unloaded length. As a novel part, the influence of the annual ring structure on the local material behavior and the global elasto-plastic force–displacement behavior of wood under compression perpendicular to the grain were numerically investigated. Hill’s failure criterion was found to be the least suitable at both length scales, local material behavior and global structural response. The Hoffman and the QMS criteria showed quite good agreement with the biaxial experiments in terms of force–displacement relations and strain distributions for different loading situations, especially for combinations with radial compression, while there was less agreement with experiments for the behavior of combinations with tangential compression. Application of these material models to compression perpendicular to the grain for studying the unloaded length effect yielded similar trends as observed in structural tests. A reasonable and similar force–displacement response by Hoffman and QMS criteria was observed, while Hill’s model yielded significantly overestimated force carrying capacity. Differences in force–displacement response for different loading situations were well in line with literature findings and the influence of the annual ring curvature on the overall force–displacement behavior could be quantified.
Highlights
The natural cellular and fibrous material wood can be considered as a cylindrically or polar orthotropic material due to its cylindrically sha ped, circular annual ring structure and differences in material properties in three principal directions: longitudinal, radial and tangential
As regards radial compression and shear in the RT-plane, Fig. 5 shows that all the numerical models predict stiffness properties very close to the unloading stiffness, since material parameters were evaluated from these parts of the experimental curve
Similar observations are made for the compressive behavior in the tangential direction, see Fig. 6
Summary
The natural cellular and fibrous material wood can be considered as a cylindrically or polar orthotropic material due to its cylindrically sha ped, circular annual ring structure and differences in material properties in three principal directions: longitudinal, radial and tangential. Considering differences in the two transverse material directions, the radial and tangential directions, are important for the understanding of corresponding phenomena and for improving engineering design rules. Due to the differences in stiffness and strength in the radial and tangential directions and the curvature of annual rings, a combined and complex stress state arises already under uniaxial compression or ten sion and becomes even more complex in case of loading under an angle to the principal material directions. This calls for a multi-axial stress analysis
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