Modeling Wood Strands as Multi-Layer Composites: Bending and Tension Loads


  • Daniel P. Hindman
  • Jong Nam Lee


Intra-ring properties, earlywood, latewood, mechanical properties


Wood strands are composed of distinct layers of earlywood and latewood material. Previous research has demonstrated that latewood mechanical properties may be two to three times greater than earlywood mechanical properties. However, wood composite modeling assumes strands are uniform, homogenous elements. This paper investigated the effect of considering wood strands as two-layer composites consisting of earlywood and latewood, or intra-ring, layers. Experimental measurement of the intra-ring properties of loblolly pine (P. taeda) provided inputs to finite element models using both solid layers and cellular layers to represent longitudinal tracheids. The models were compared with three different types of strands cut at various orientations (flatsawn, quartersawn, non-aligned cut) in both tension and bending loadings. The model prediction of strand stiffness greatly improved by considering the strands as 2-layer composites compared to homogenous sections. Further improvements of the prediction of stiffness were made from modeling cellular layers rather than solid layers. The rule of mixtures predictions of stiffness produced good agreement for the non-aligned strands in both tension and bending loading, but only good agreement in the tension loading for the flatsawn strand. Examining the stress distributions of the strands from the finite element model, the solid models showed distinct stress changes at the edges of the intra-ring layers, indicating stress concentrations at the boundaries of the intra-ring layers. The cellular models showed a much more gradual stress transition between the intra-ring layers, which is a more realistic scenario.


ASTM. 2004. Standard test methods for small clear specimens of timber. ASTM D 143-94. Annual Book of ASTM Standards. Vol. 4.10. ASTM, West Conshohocken, PA. 800 pp.nBodig, J., and B. A. Jayne. 1982. Mechanics of wood and wood composites. Kreiger Publishing Company, Malabar, Florida. 712 pp.nCramer, S., D. Kretschmann, R. Lakes, and T. Schmidt. 2005. Earlywood and latewood elastic properties of loblolly pine. Holzforschung 59:531-538.nDumail, J.-F., and L. Salmén. 2001. Intra-ring variations in the rolling shear modulus of spruce wood. Holzforschung 55(5):549-553.nFarruggia, F., and P. Perré. 2000. Microscopic tensile tests in the transverse plane of earlywood and latewood parts of spruce. Wood Sci. Technol. 34:65-82.nGere, J. M., and S. Timoshenko. 1997. Mechanics of materials. Fourth Edition. PWS Publishing Company, New York, NY. 912 pp.nGibson, L. J. 2005. Biomechanics of cellular solids. Biomechanics. 38:377-399.nGroom, L., L. Mott, and S. Shaler. 2002. Mechanical properties of individual southern pine fibers. Part I. Determination and variability of stress-strain curves with respect to tree height and juvenility. Wood Fiber Sci. 34(1):14-27.nGrotta, A. T., R. J. Leichti, B. L. Gartner, and G. R. Johnson. 2005. Effect of growth ring orientation and placement of earlywood and latewood on MOE and MOR of very small clear Douglas-fir beams. Wood Fiber Sci. 37(2):207-212.nHepworth, D. G., and J. F. V. Vincent. 1998. Modeling the mechanical properties of xylem tissue from tobacco plants (Nicotiana tabacum ‘Samsun’) by considering the importance of molecular and micromechanisms. Annals Botany 81:761-770.nJayne, B. A. 1959. Mechanical properties of wood fibers. Tappi 42(6):461-467.nJones, R. M. 1999. Mechanics of composite materials. Second Edition. Taylor and Francis, Inc, Philadelphia, PA. 519 pp.nLarson, P. R., D. E. Kretschmann, A. Clark III, and J. G. Isebrands. 2001. Formation and properties of juvenile wood in southern pines. FPL-GTR-129. USDA Forest Service. Madison, WI. 42 pp.nMegraw, R., D. Bremer, G. Leaf, and J. Roers. 1999. Stiffness in loblolly pine as a function of ring position and height, and its relationship to microfibril angle and specific gravity. Pages 341-349 in Nepveu, G., ed. Proc. IUFRO WP S5.01-04 Third Workshop on Connection Between Silviculture and Wood Quality through Modeling Approaches and Simulation Software, La Londe-les-Maures, Sept. 1999, Publication Equipe de Recherches sur la Qualité de Bois 1992/2, Dec., INRA-Nancy, France.nMott, L., L. Groom, and S. Shaler. 2002. Mechanical properties of individual southern pine fibers. Part II. Comparison of earlywood and latewood fibers with respect to tree height and juvenility. Wood Fiber Sci. 34(2):221-237.nSalmén, L. 2004. Micromechanical understanding of the cell-wall structure. C. R. Biologies 327:873-880.nTriche, M. H., and M. O. Hunt. 1993. Modeling of parallelaligned wood strand composites. Forest Prod. J. 43(11/12): 33-44.nWang, Y.-T., and F. Lam. 1998. Computational modeling of material failure for parallel-aligned strand based wood composites. Computational Materials Science 11:157-165.nZombori, B. G., F. A. Kamke, and L. T. Watson. 2001. Simulation of the mat formation process. Wood Fiber Sci. 33(4):564-579.n






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