OPEN ACCESS
This paper is concerned with the evaluation of effective material properties of wood. Since both mechanical loading and climatic changes play a crucial role in the prediction of wood response, we consider not only stiffness, but also non-mechanical properties driving the heat and moisture transport and thus indirectly addressing the swelling and shrinkage properties of wood. In this regard, classical micromechanical models as well as numerical simulations based on the Extended Finite Element Method are examined. A special attention is devoted to the influence of microstructural details of the porous phase. To that end, the X-ray computational micro-tomography is adopted when seeking for information beyond the volume fraction of phases that can be identified at various levels of a hierarchical arrangement of wood. A spruce wood is selected as one particular example to compare individual computational approaches.
Conductivity, diffusivity, homogenization, microfibril angle, micro-tomography, Mori-Tanaka method, nanoindentation, stiffness, X-FEM
[1] Ormarsson, S. & Dahlblom, O., Finite element modelling of moisture related and visco-elastic deformations in inhomogeneous timber beams. Engineering Structures, 49, pp. 182–89, 2013. https://doi.org/10.1016/j.engstruct.2012.10.019
[2] Fortino, S., Mirianon, F. & Toratti, T., A 3d moisture-stress FEM analysis for time dependent problems in timber structures. Mechanical and Time-Dependendent Materials, 13(4), pp. 333–56, 2009. https://doi.org/10.1007/s11043-009-9103-z
[3] Dang, D., Moutou Pitti, R., Toussaint, E. & Grédiac, M., Investigating wood under thermo- hydromechanical loading at the ring scale using full-field measurements. Wood Science and Technology, 52(6), pp. 1473–93, 2018. https://doi.org/10.1007/s00226-018-1051-9
[4] Rafsanjani, A., Lanvermann, C., Niemz, P., Carmeliet, J. & Derome, D., Musltiscale analysis of free swelling of Norway spruce. Composites: Part A, 54, pp. 70–78, 2013. https://doi.org/10.1016/j.compositesa.2013.07.005
[5] Šejnoha, M., Sýkora, J., Vorel, J., Kucíková, L., Antoš, J., Pokorný, J. & Pavlík, Z., Moisture induced strains in spruce from homogenization and transient moisture transport analysis. Computers and Structures, 2018. Submitted.
[6] Melzerová, L., Kucíková, L., Janda, T. & Šejnoha, M., Estimation of orthotropic mechanical properties of wood based on non-destructive testing. Wood Research, 61(6), pp. 861–70, 2016.
[7] Šejnoha, M., Janda, T., Melzerová, L., Nežerka, V. & Šejnoha, J., Modeling glulams in linear range with parameters updated using Bayesian inference. Engineering Structures, 138, pp. 293–307, 2017. https://doi.org/10.1016/j.engstruct.2017.02.021
[8] Šejnoha, M., Kucíková, L., Vorel, J., Hrbek, V. & Němeček, J., Comparing nano and macroindentation in search for microfibril angle in spruce. Internationl Journal of Computational Methods and Experimental Measurements, 5(2), pp. 135–43, 2017. https://doi.org/10.2495/cmem-v5-n2-135-143
[9] Šejnoha, M., Janda, T., Vorel, J., Kucíková, L. & Padevěd, P., Combining homoge- nization, indentation and bayesian inference in estimating the microfibril angle of spruce. Procedia Engineering, 190, pp. 310–17, 2017. https://doi.org/10.1016/j.pro- eng.2017.05.343
[10] Jäger, A., Bader, T., Hofstetter, K. & Eberhardsteiner, J., The relation between indentation modulus, microfibril angle, and elastic properties of wood cell walls. Compos- ites Part A: Applied Science and Manufacturing, 42(6), pp. 677–85, 2011. https://doi. org/10.1016/j.compositesa.2011.02.007
[11] Persson, K., Micromechanical Modelling of Wood and Fibre Properties. Ph.D. thesis, Publ. TVSM-1013, Div. of Struc. Mech., Lund University, 2000.
[12] Eitelberger, J. & Hofstetter, K., Prediction of transport properties of wood below the fiber saturation point–a multiscale homogenization approach and its experimental validation: Part I: thermal conductivity. Composites Science and Technology, 71(2), pp. 134–44, 2011. https://doi.org/10.1016/j.compscitech.2010.11.007
[13] Eitelberger, J. & Hofstetter, K., Prediction of transport properties of wood below the fiber saturation point a multiscale homogenization approach and its experimental validation. part II: Steady state moisture diffusion coefficient. Composites Science and Technology, 71(2), pp. 145–51, 2011. https://doi.org/10.1016/j.compscitech.2010.11.006
[14] Benveniste, Y., A new approach to the application of Mori-Tanaka theory in composite materials. Mechanics of Materials, 6(2), pp. 147–57, 1987. https://doi.org/10.1016/0167- 6636(87)90005-6
[15] Šejnoha, M. & Zeman, J., Micromechanics in Practice. WIT Press, Southampton, Boston, 2013.
[16] Hofstetter, K., Hellmich, C. & Eberhardsteiner, J., Development and experimental validation of a continuum micromechanics model for the elasticity of wood. European Journal of Mechanics -A/Solids, 24(6), pp. 1030–1053, 2005. https://doi.org/10.1016/j. euromechsol.2005.05.006
[17] Vorel, J., Sýkora, J., Urbanova, S. & Šejnoha, M., From CT scans of wood to_nite element meshes. Proceedings of the The Fifteenth International Conferenceon Civil, Structural and Environmental Engineering Computing, Prague, CzechRepublic, ed. B.
Topping, Civil-Comp Press, 2015. https://doi.org/10.4203/ccp.108.221
[18] Tze, W.T.Y., Wang, S., Rials, T.G., Pharr, G.M. & Kelley, S.S., Nanoindentation of wood cell walls: Continuous stiffness and hardness measurements. Composites: Part A, 38(3), pp. 945–53, 2007. https://doi.org/10.1016/j.compositesa.2006.06.018
[19] Gamstedt, E.K., Bader, T.K. & de Borst, K., Mixed numerical-experimental methods in wood micromechanics. Wood Science and Technology, 47(1), pp. 183–202, 2013. https://doi.org/10.1007/s00226-012-0519-2
[20] Vlassak, J. & Nix, W., Measuring the elastic properties of anisotropic materials by means of indentation experiments. Journal of the Mechanics and Physics of Solids, 42(8), pp. 1223–45, 1994. https://doi.org/10.1016/0022-5096(94)90033-7
[21] Vlassak, J., Ciavarella, M., Barber, J. & Wang, X., The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. Journal of the Mechanics and Physics of Solids, 51(9), pp. 1701–21, 2003. https://doi.org/10.1016/0022-5096(94)90033-7
[22] Arifin, A.Z. & Asano, A., Image segmentation by histogarm thresholding using hierarchical cluster analysis. Pattern Recognition Letters, 27, pp. 1515–21, 2006. https://doi. org/10.1016/j.patrec.2006.02.022
[23] Fíla, T., Kumpová, I., Koudelka, P., Zlámal, P., Vavřík, D., Jiroušek, O. & Jung, C., Dual-energy x-ray micro-ct imaging of hybrid Ni/Al. 7th International Workshop on Radiation Imaging Detectors 28 June-2 July 2015, DESY, Hamburg, Germany, 2015. https://doi.org/10.1088/1748-0221/11/01/c01005
[24] Benveniste, Y., Dvorak, G.J. & Chen, T., On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. Journal of the Mechanics and Physics of Solids, 39(7), pp. 927–46, 1991. https://doi.org/10.1016/ 0022-5096(91)90012-d
[25] Kucíková, L., Vorel, J., Sýkora, J. & Šejnoha, M., Effective heat and moisture transport properties of spruce. 23rd International conference Engineering Mechanics 2017, 2017.
[26] Teplý, J.L. & Dvorak, G.J., Bound on overall instantaneous properties of elastic-plastic composites. Journal of the Mechanics and Physics of Solids, 36(1), pp. 29–58, 1988. https://doi.org/10.1016/0022-5096(88)90019-1
[27] Michel, J.C., Moulinec, H. & Suquet, P., Effective properties of composite materials with periodic microstructure: A computational approach. Computer Methods in Applied Mechanics and Engineering, 172(1–4), pp. 109–143, 1999. https://doi.org/10.1016/ s0045-7825(98)00227-8
[28] Fish, J. & Shek, K., Multiscale analysis of large-scale nonlinear structures and materials. International Journal for Computational Civil and Structural Engineering, 1(1), pp. 79–90, 2000.
[29] Kouznetsova, V., Geers, M.G.D. & Brekelmans, W.A.M., Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogeni- zation scheme. International Journal for Numerical Methods in Engineering, 54(8), pp. 1235–1260, 2002. https://doi.org/10.1002/nme.541
[30] Zeman, J. & Šejnoha, M., From random microstructures to representative volume elements. Modelling and Simulation in Materials Science and Engineering, 15(4), pp. S325–S335, 2007. https://doi.org/10.1088/0965-0393/15/4/s01
[31] Vorel, J., Grippon, E. & Šejnoha, M., Effective thermoelastic properties of polysilox- ane matrix based plain weave textile composites. International Journal for Multiscale Computational Engineering, 13(3), pp. 181–200, 2015. https://doi.org/10.1615/intj- multcompeng.2014011020
[32] Moës, N., Cloirec, M., Cartraud, P. & Remacle, J.F., A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering, 192(28–30), pp. 3163–77, 2003. https://doi.org/10.1016/s0045- 7825(03)00346-3
[33] Sukumar, N., Chopp, D.L., Moës, N. & Belytschko, T., Modeling holes and inclusions by level sets in the extened finite element method. Computer Methods in Applied Mechanics and Engineering, 190(46–47), pp. 6183–200, 2001. https://doi.org/10.1016/ s0045-7825(01)00215-8
[34] Vaziri, M., du Plessis, A., Sandberg, D. & Berg, S., Nano x-ray tomography analysis of the cell-wall density of welded beech joints. Wood Material Science and Engineering, 2015. https://doi.org/10.1080/17480272.2015.1062418
[35] Kettunen, P.O., Wood: Structure and Properties. Trans Tech Publications Ltd, Uetikon- Zuerich, 2006.
[36] Šejnoha, M., Janda, T., Vorel, J., Kucíková, L., Padevět, P. & Hrbek, V., Bayesian inference as a tool for improving predictions of effective elastic properties of wood. Computers and Structures, 2018. Submitted.