Interaction and multiscale mechanics

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Determination of the linear elastic stiffness and hygroexpansion of softwood by a multilayered unit cell using poromechanics

  • Gloimuller, Stefan (Institute for Mechanics of Materials and Structures, Vienna University of Technology) ;
  • de Borst, Karin (Institute for Mechanics of Materials and Structures, Vienna University of Technology) ;
  • Bader, Thomas K. (Institute for Mechanics of Materials and Structures, Vienna University of Technology) ;
  • Eberhardsteiner, Josef (Institute for Mechanics of Materials and Structures, Vienna University of Technology)
  • Received : 2011.08.17
  • Accepted : 2012.08.27
  • Published : 2012.09.25
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Abstract

Hygroexpansion of wood is a known and undesired characteristic in civil engineering. When wood is exposed to changing environmental humidity, it adsorbs or desorbs moisture and warps. The resulting distortions or - at restrained conditions - cracks are a major concern in timber engineering. We herein present a multiscale model for prediction of the macroscopic hygroexpansion behavior of individual pieces of softwood from their microstructure, demonstrated for spruce. By applying poromicromechanics, we establish a link between the swelling pressure, driving the hygroexpansion of wood at the nanoscale, and the resulting macroscopic dimensional changes. The model comprises six homogenization steps, which are performed by means of continuum micromechanics, the unit cell method and laminate theory, all formulated in a poromechanical framework. Model predictions for elastic properties of wood as functions of the moisture content closely approach corresponding experimental data. As for the hygroexpansion behavior, the swelling pressure has to be back-calculated from macroscopic hygroexpansion data. The good reproduction of the anisotropy of wood hygroexpansion, based on only a single scalar calibration parameter, underlines the suitability of the model. The multiscale model constitutes a valuable tool for studying the effect of microstructural features on the macroscopic behavior and for assessing the hygroexpansion behavior at smaller length scales, which are inaccessible to experiments. The model predictions deliver input parameters for the analysis of timber at the structural scale, therewith enabling to optimize the use of timber and to prevent moisture-induced damage or failure.

Keywords

References

  1. Astley, R., Stol, K. and Harrington, J.J. (1998), "Modelling the elastic properties of softwood, part ii: The cellular microstructure", Holz Roh Werkst., 56(1), 43-50. https://doi.org/10.1007/s001070050262
  2. Bader, T.K., Hofstetter, K. and Eberhardsteiner, J. (2011), "The poroelastic role of water in cell walls of the hierarchical composite "softwood", Acta Mech., 217(1-2), 75-100. https://doi.org/10.1007/s00707-010-0368-8
  3. Bengtsson, C. (2001), "Variation of moisture induced movements in norway spruce (picea abies)", Ann. Forest Sci., 58(5), 569-581.
  4. Bergander, A. (2001), Local variability in chemical and physical properties of spruce wood fibers, Doctoral thesis, Royal Institute of Technology.
  5. Biot, M.A. (1955), "Theory of elasticity and consolidation for a porous anisotropic solid", J. Appl. Phys., 26(2), 182-185. https://doi.org/10.1063/1.1721956
  6. Bohm, H. (2004), A short introduction to continuum micromechanics, Springer Verlag, Wien, New York.
  7. Boutelje, J.B. (1962), "The relationship of structure to transverse anisotropy in wood with reference to shrinkage and elasticity", Holzforschung, 16(2), 33-46. https://doi.org/10.1515/hfsg.1962.16.2.33
  8. Burgert, I. (2000), Die mechanische bedeutung der holzstrahlen im lebenden baum, Doctoral thesis, University Hamburg.
  9. Burgert, I. (2003), "Uber die mechanische bedeutung der holzstrahlen", Schweiz. Z. Forstwes., 154(12), 498-503. https://doi.org/10.3188/szf.2003.0498
  10. Derome, D., Griffa, M., Koebel, M. and Carmeliet, J. (2011), "Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography", J. Struct. Biol., 173(1), 180-190. https://doi.org/10.1016/j.jsb.2010.08.011
  11. Dormieux, L., Molinari, A. and Kondo, D. (2002), "Micromechanical approach to the behavior of poroelastic material", J. Mech. Phy. Solids, 50(10), 2203-2231. https://doi.org/10.1016/S0022-5096(02)00008-X
  12. Eitelberger, J. and Hofstetter, K. (2011), "Prediction of transport properties of wood below the fiber saturation point -a multiscale homogenization approach and its experimental validation, part I: Thermal conductivity", Compos. Sci. Technol., 71(2), 134-144. https://doi.org/10.1016/j.compscitech.2010.11.007
  13. El Omri, A., Fennan, A., Sidoro., F. and Hihi, A. (2000), "Elastic-plastic homogenization for layered composites", Eur. J. Mech. A-Solid., 19(4), 585-601. https://doi.org/10.1016/S0997-7538(00)00182-0
  14. Elwood, E. (1954), Properties of american beech in tension and compression perpendicular to the grain and their relation to drying, Yale Univ. School For., Bull. No. 61, Yale Univ., New Haven, CT.
  15. Farruggia, F. and Perré, P. (2000), "Microscopic tensile tests in the transverse plane of earlywood and latewood parts of spruce", Wood Sci. Technol., 34(2), 65-82. https://doi.org/10.1007/s002260000034
  16. Fengel, D. and Wegener, G. (1983), WOOD Chemistry, Ultrastructure, Reactions, Verlag Kessel, Munich.
  17. Fratzl, P. and Weinkamer, R. (2007), "Nature's hierarchical material", Prog. Mater. Sci., 52(8), 1263-1334. https://doi.org/10.1016/j.pmatsci.2007.06.001
  18. Gloimüller, S. (2012), Multiscale modeling and experimental investigation of the hygroexpansion behavior of softwood, Doctoral thesis, Vienna University of Technology, Faculty of Civil Engineering. In English.
  19. Greenhill, W. (1936), "Strength tests perpendicular to the grain of timber at various temperautres and moisture contents", J. Counc. Sci. Ind. Res., 9(4), 265-278.
  20. Hellmich, C. and Ulm, F.J. (2005), "Drained and undrained poroelastic properties of healthy and pathological bone: A poro-micromechanical investigation", Transport Porous Med., 58(3), 243-268. https://doi.org/10.1007/s11242-004-6298-y
  21. Hofstetter, K., Hellmich, C. and Eberhardsteiner, J. (2006), "Micromechanical modeling of solid-type and platetype deformation patterns within softwood materials. A review and an improved approach", Holzforschung, 61(4), 343-351.
  22. Kadita, S., Yamada, T., Suzuki, M. and K., K. (1961), "Studies on the rheological properties of wood. i. effect of moisture content on the dynamic young's modulus of wood. ii. effect of heat-treating condition on the hygroscopicity and dynamic young's modulus of wood", J. Jap. Wood Res. Soc., 7(1), 29-38.
  23. Kifetew, G. (1997), "Application of the earlywood-latewood interaction theory to the shrinkage anisotropy of scots pine", International Conference of COST Action E8, Mechanical Performance of Wood and Wood Products, Theme: Wood-water relations, Royal Institute of Technology Stockholm, Sweden.
  24. Kifetew, G., Lindberg, H. and Wiklung, M. (1997), "Tangential and radial deformation field measurements on wood during drying", Wood Sci. Technol., 31(1), 35-44. https://doi.org/10.1007/BF00705698
  25. Kollmann, F. (1951), Technologie des holzes und der holzwerkstoffe, Verlag Springer, Berlin, Heidelberg, New York.
  26. Kufner, M. (1978), "Modulus of elasticity and tensile strength of wood species with different density and their dependence on moisture content", Holz Roh. Werkst., 36(11), 435-439. https://doi.org/10.1007/BF02607685
  27. Lindstrom, H. (1996), "Fiber length, tracheid diameter, and latewood percentage in norway spruce: Development from pith outwards", Wood Fiber Sci., 29(1), 21-34.
  28. Marklund, E. and Varna, J. (2009), "Modeling the hygroexpansion of aligned wood fiber composites", Compos. Sci. Technol., 69(7-8), 1108-1114. https://doi.org/10.1016/j.compscitech.2009.02.006
  29. Moden, C.S. and Berglund, L.A. (2008a), "Elastic deformation mechanisms of softwoods in radial tension -cell wall bending or stretching?", Holzforschung, 62(5), 562-568.
  30. Moden, C.S. and Berglund, L.A. (2008b), "A two-phase annual ring model of transverse anisotropy in softwoods", Compos. Sci. Technol., 68(14), 3020-3026. https://doi.org/10.1016/j.compscitech.2008.06.022
  31. Nakano, T. (2008), "Analysis of cell wall swelling on the basis of a cylindrical model", Holzforschung, 62(3), 352-356.
  32. Neagu, R. and Gamstedt, E. (2007), "Modelling of effects of ultrastructural morphology on the hygroelastic properties of wood fibres", J. Mater. Sci., 42(24), 10254-10274. https://doi.org/10.1007/s10853-006-1199-9
  33. Neuhaus, T.H. (1981), Elastizitatszahlen von fichtenholz in abhangigkeit von der holzfeuchte, Technischwissenschaftliche Mitteilungen 81-8, Insitut fur Konstruktiven Ingenieurbau, Ruhr-Universitat Bochum.
  34. Noack, D., Schwab, E. and Bartz, A. (1973), "Characteristics for a judgment of the sorption and swelling behavior of wood", Wood Sci. Technol., 7(3), 218-236. https://doi.org/10.1007/BF00355552
  35. Olsson, T., Megnis, M., Varna, J. and Lindberg, H. (2001), "Study of the transverse liquid .ow paths in pine and spruce using scanning electron microscopy", J. Wood Sci., 47(4), 282-288. https://doi.org/10.1007/BF00766714
  36. Pang, S. (2002), "Predicting anisotropic shrinkage of softwood part 1: Theories", Wood Sci. Technol., 36(1), 75-91. https://doi.org/10.1007/s00226-001-0122-4
  37. Pang, S. and Herritsch, A. (2005), "Physical properties of earlywood and latewood of pinus radiata d. don: Anisotropic shrinkage, equilibrium moisture content and .bre saturation point", Holzforschung, 59, 654-661.
  38. Perre, P. and Huber, F. (2007), "Measurement of free shrinkage at the tissue level using an optical microscope with an immersion objective: results obtained for douglas fir (pseudotsuga menziesii) and spruce (picea abies)", Ann. Forest Sci., 64(3), 255-265. https://doi.org/10.1051/forest:2007003
  39. Persson, K. (2000), Micromechanical modelling of wood and fibre properties, Doctoral thesis, Lund University. In English.
  40. Qing, H. and Mishnaevsky Jr., L. (2008), 3d hierarchical computational model of wood as a cellular material with .bril reinforced, heterogeneous multiple layers, Mechanics of Materials.
  41. Qing, H. and Mishnaevsky Jr., L. (2009), Moisture-related mechanical properties of softwood: 3d micromechanical modeling, Computational Materials Science.
  42. Schneider, A. (1971), "Investigations on the influence of heat treatments with a range of temperatures from $200^{\circ}$ to $200^{\circ}C$ on the modulus of elasticity, maximum crushing strength, and impact work of pine sapwood and beechwood", Holz Roh. Werkst, 29(11), 431-440. https://doi.org/10.1007/BF02625823
  43. Siimes, F. (1967), "The effect of specific gravity, moisture content, temperature and heating time on the tension and compression strength and elastic properties perpendicular to the grain of .nnish pine, spruce and birch wood and the signi.cance of those factors on the checking of timber at kiln drying", State Inst. Tech. Res., Helsinki, Finland, 84.
  44. Smith, S.A. and Langrish, T.A.G. (2008), "Multicomponent solid modeling of continuous and intermittent drying of pinus radiata sapwood below the fiber saturation point", Dry. Technol., 26(7), 844-854. https://doi.org/10.1080/07373930802136012
  45. Sulzberger, P. (1953), The effect of temperature on the strength of wood, plywood and glue joints, Aeronaut. Res. Consultative Com. Rep. ACA-46, Melbourne, Australia.
  46. Tarmian, A. and Azadfallah, M. (2009), "Variation of cell features and chemical composition in spruce consisting of opposite, normal, and compression wood", BioResource., 4(1), 194-204.
  47. Ulm, F.J., Delafargue, A. and Constantinides, G. (2004), "Experimental microporomechanics", Lecture notes prepared for the summer school Applied Micromechanics of Porous Materials, Coordinated by L. Dormieux and F.-J. Ulm, International Centre for Mechanical Sciences (CISM), Udine, Italy.
  48. USDA (1999), Wood handbook, U.S. Department of Agriculture, United States of America.
  49. Wagenführ, R. (2007), Holzatlas, Fachbuchverlag Leipzig im Carl Hanser Verlag, Leipzig, 6. edition.
  50. Watanabe, U., Fujita, M. and Norimoto, M. (2002), "Transverse young's moduli and cell shapes in coniferous early wood", Holzforschung, 56(1), 1-6. https://doi.org/10.1515/HF.2002.001
  51. Wilson, R. (1932), Strength-moisture relations of wood, USDA Tech. Bull. No. 282 U.S. Dep. Agric., Washington, D.C.
  52. Yamamoto, H. (1999), "A model of the anisotropic swelling and shrinking process of wood. Part 1: Generalization of Barber's wood fiber model", Wood Sci. Technol., 33(4), 311-325. https://doi.org/10.1007/s002260050118
  53. Zaoui, A. (2002), "Continuum micromechanics: Survey", J. Eng. Mech., 128(8), 808-816. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(808)

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