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Licensed Unlicensed Requires Authentication Published by De Gruyter January 8, 2021

Voxel-based finite element modelling of wood elements based on spatial density and geometry data using computed tomography

  • Jens U. Hartig ORCID logo EMAIL logo , André Bieberle ORCID logo , Chris Engmann and Peer Haller
From the journal Holzforschung

Abstract

In this paper, voxel-based finite element modelling based on spatial geometry and density data is applied to simulate the detailed stress and strain distribution in a large wood element. As example, a moulded wooden tube with a length of 3 m and a diameter of 0.3 m is examined. Gamma-ray computed tomography is used to obtain both, its actual geometric shape and spatial density distribution. Correlation functions (R2 ≈ 0.6) between density and elastic material properties are experimentally determined and serve as link for defining the non-uniform distribution of the material properties in the finite element model. Considering the geometric imperfections and spatial variation of the material properties, a detailed analysis of the stress and strain distribution of a wood element is performed. Additionally, a non-destructive axial compression test is applied on the wooden tube to analyse the load-bearing behaviour. By means of digital image correlation, the deformation of the surface is obtained, which also serves for validation of the finite element model in terms of strain distributions.


Corresponding author: Jens U. Hartig, Technische Universität Dresden, School of Civil and Environmental Engineering, Faculty of Civil Engineering, Institute of Steel and Timber Construction, 01062Dresden, Germany, E-mail:

Acknowledgements

Some of the simulations were performed on the Bull HPC-Cluster (HRSK-II) at the Centre for Information Services and High Performance Computing (ZIH) of Technische Universität Dresden.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Bieberle, A., Schleicher, E., and Hampel, U. (2010). Temperature control design for a high resolution gamma-ray tomography detector. Rev. Sci. Instrum. 81: 014702, https://doi.org/10.1063/1.3280184.Search in Google Scholar

Bieberle, A., Engmann, C., Hartig, J., and Haller, P. (2018). Analysis of moulded wood tube structure using gamma-ray computed tomography [Data set]. Rodare, https://doi.org/10.14278/rodare.55.Search in Google Scholar

DIN 68364. (2003). Properties of wood species – density, modulus of elasticity and strength.Search in Google Scholar

Dömény, J., Čermák, P., Koiš, V., Tippner, J., and Rousek, R. (2018). Density profile and microstructural analysis of densified beech wood (Fagus sylvatica L.) plasticized by microwave treatment. Eur. J. Wood Prod. 76: 105–111, doi:https://doi.org/10.1007/s00107-017-1173-z.Search in Google Scholar

Donaldson, L. (2008). Microfibril angle: measurement, variation and relationships – a review. IAWA J. 29: 345–386, https://doi.org/10.1163/22941932-90000192.Search in Google Scholar

EN 408. (2012). Timber structures. Structural timber and glued laminated timber. Determination of some physical and mechanical properties.Search in Google Scholar

Fernandes Diniz, J.M.B., Gil, M.H., and Castro, J.A.A.M. (2004). Hornification – its origin and interpretation in wood pulps. Wood Sci. Technol. 37: 489–494, https://doi.org/10.1007/s00226-003-0216-2.Search in Google Scholar

Forsberg, F., Mooser, R., Arnold, M., Hack, E., and Wyss, P. (2008). 3D micro-scale deformations of wood in bending: synchrotron radiation µCT data analyzed with digital volume correlation. J. Struct. Biol. 164: 255–262, https://doi.org/10.1016/j.jsb.2008.08.004.Search in Google Scholar

Forsberg, F., Sjödahl, M., Mooser, R., Hack, E., and Wyss, P. (2010). Full three-dimensional strain measurements on wood exposed to three-point bending: analysis by use of digital volume correlation applied to synchrotron radiation micro-computed tomography image data. Strain 46: 47–60, https://doi.org/10.1111/j.1475-1305.2009.00687.x.Search in Google Scholar

Gilbert, B.P., Underhill, I.D., Fernando, D., Bailleres, H., and Miller, D. (2018). Structural behaviour of hardwood veneer-based circular hollow sections of different compactness. Construct. Build. Mater. 170: 557–569, https://doi.org/10.1016/j.conbuildmat.2018.03.105.Search in Google Scholar

Groß, K., Bieberle, A., Gladyszewski, K., Schubert, M., Hampel, U., Skiborowski, M., and Gorak, A. (2019). Analysis of flow patterns in high-gravity equipment using gamma-ray computed tomography. Chem. Ing. Tech. 91: 1032–1040, https://doi.org/10.1002/cite.201800085.Search in Google Scholar

Haller, P. (2007). Concepts for textile reinforcements for timber structures. Mater. Struct. 40: 107–118, https://doi.org/10.1617/s11527-006-9153-5.Search in Google Scholar

Hampel, U., Bieberle, A., Hoppe, D., Kronenberg, J., Schleicher, E., Sühnel, T., Zimmermann, F., and Zippe, C. (2007). High resolution gamma ray tomography scanner for flow measurement and non-destructive testing applications. Rev. Sci. Instrum. 78: 103704, https://doi.org/10.1063/1.2795648.Search in Google Scholar

Härting, H.-U., Bieberle, A., Lange, R., Larachi, F., and Schubert, M. (2015). Hydrodynamics of co-current two-phase flow in an inclined rotating tubular fixed bed reactor – wetting intermittency via periodic catalyst immersion. Chem. Eng. Sci. 28: 147–158, https://doi.org/10.1016/j.ces.2015.02.008.Search in Google Scholar

Hartig, J.U., Wehsener, J., and Haller, P. (2016). Experimental and theoretical investigations on moulded wooden tubes made of beech (Fagus sylvatica L.). Construct. Build. Mater. 126: 527–536, https://doi.org/10.1016/j.conbuildmat.2016.09.042.Search in Google Scholar

Heiduschke, A. and Haller, P. (2010). Fiber-reinforced plastic-confined wood profiles under axial compression. Struct. Eng. Int. 20: 246–253, https://doi.org/10.2749/101686610792016772.Search in Google Scholar

Kak, C. and Slaney, M. (1988). Principles of computerized tomographic imaging. New York: IEEE Press.Search in Google Scholar

Keyak, J.H., Meagher, J.M., Skinner, H.B., and Mote, C.D. (1990). Automated three-dimensional finite element modelling of bone: a new method. J. Biomed. Eng. 12: 389–397, https://doi.org/10.1016/0141-5425(90)90022-f.Search in Google Scholar

Kollmann, F. and Krech, H. (1960). Dynamische Messung der elastischen Holzeigenschaften und der Dämpfung. Ein Beitrag zur zerstörungsfreien Werkstoffprüfung. Holz. Roh. Werkst. 18: 41–54, https://doi.org/10.1007/bf02615616.Search in Google Scholar

Kollmann, F.F.P. and Côté, J.W.Jr. (1968). Principles of wood science and technology. Part I: solid wood. Berlin: Springer-Verlag.10.1007/978-3-642-87928-9Search in Google Scholar

Konopka, D., Ehricht, S., and Kaliske, M. (2019). Hygro-mechanical investigations of clavichord replica at cyclic climate load: experiments and simulations. J. Cult. Herit. 36: 210–221, https://doi.org/10.1016/j.culher.2018.07.006.Search in Google Scholar

Kutnar, A., Sandberg, D., and Haller, P. (2015). Compressed and moulded wood from processing to products – a review. Holzforschung 69: 885–897, https://doi.org/10.1515/hf-2014-0187.Search in Google Scholar

Lengsfeld, M., Schmitt, J., Alter, P., Kaminsky, J., and Leppek, R. (1998). Comparison of geometry-based and CT voxel-based finite element modelling and experimental validation. Med. Eng. Phys. 20: 515–522, https://doi.org/10.1016/s1350-4533(98)00054-x.Search in Google Scholar

Luo, P.F., Chao, Y.J., Sutton, M.A., and Peters, W.H.III. (1993). Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision. Exp. Mech. 33: 123–132, https://doi.org/10.1007/bf02322488.Search in Google Scholar

Macedo, A., Vaz, C., Pereira, J., Naime, J., Cruvinel, P., and Crestana, S. (2002). Wood density determination by X- and gamma-ray tomography. Holzforschung 56: 535–540, https://doi.org/10.1515/hf.2002.082.Search in Google Scholar

Neumann, M., Schäfer, T., Bieberle, A., and Hampel, U. (2016). An experimental study on the gas entrainment in horizontally and vertically installed centrifugal pumps. J. Fluid Eng. 138: 091301, https://doi.org/10.1115/1.4033029.Search in Google Scholar

Onoe, M., Tsao, J., Yamada, H., Nakamura, H., Kogure, J., Kawamura, H., and Yoshimatsu, M. (1984). Computed tomography for measuring the annual rings of a live tree. Nucl. Instrum. Methods Phys. Res. 221: 213–220, https://doi.org/10.1016/0167-5087(84)90202-3.Search in Google Scholar

Ozyhar, T., Hering, S., and Niemz, P. (2012). Moisture-dependent elastic and strength anisotropy of European beech wood in tension. J. Mater. Sci. 47: 6141–6150, https://doi.org/10.1007/s10853-012-6534-8.Search in Google Scholar

Palenstijn, W.J., Batenburg, K.J., and Sijbers, J. (2011). Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs). J. Struct. Biol. 176: 250–253, https://doi.org/10.1016/j.jsb.2011.07.017.Search in Google Scholar

Pernkopf, M., Riegler, M., and Gronalt, M. (2019). Profitability gain expectations for computed tomography of sawn logs. Eur. J. Wood Wood Prod. 77: 619–631, https://doi.org/10.1007/s00107-019-01414-x.Search in Google Scholar

Sandberg, D., Haller, P., and Navi, P. (2013). Thermo-hydro and thermo-hydro-mechanical wood processing: an opportunity for future environmentally friendly wood products. Wood Mater. Sci. Eng. 8: 1–25, https://doi.org/10.1080/17480272.2012.751935.Search in Google Scholar

Schubert, M., Bieberle, A., Barthel, F., Boden, S., and Hampel, U. (2011). Advanced tomographic techniques for flow imaging in columns with flow distribution packings. Chem. Ing. Tech. 83: 979–991, https://doi.org/10.1002/cite.201100022.Search in Google Scholar

Sutton, M.A., Yan, J.H., Tiwari, V., Schreier, H.W., and Orteu, J.J. (2008). The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt. Laser. Eng. 46: 746–757, https://doi.org/10.1016/j.optlaseng.2008.05.005.Search in Google Scholar

Tschentscher, R., Schubert, M., Bieberle, A., Nijhuis, T.A., van der Schaaf, J., Hampel, U., and Schouten, J.C. (2011). Tomography measurements of gas holdup in rotating foam reactors with Newtonian, non-Newtonian and foaming liquids. Chem. Eng. Sci. 66: 3317–3327, https://doi.org/10.1016/j.ces.2011.01.051.Search in Google Scholar

van Aarle, W., Palenstijn, W.J., De Beenhouwer, J., Altantzis, T., Bals, S., Batenburg, K.J., and Sijbers, J. (2015). The ASTRA toolbox: a platform for advanced algorithm development in electron tomography. Ultramicroscopy 157: 35–47, https://doi.org/10.1016/j.ultramic.2015.05.002.Search in Google Scholar

van Aarle, W., Palenstijn, W.J., Cant, J., Janssens, E., Bleichrodt, F., Dabravolski, A., De Beenhouwer, J., Batenburg, K.J., and Sijbers, J. (2016). Fast and flexible X-ray tomography using the ASTRA toolbox. Opt. Express 24: 25129–25147, https://doi.org/10.1364/oe.24.025129.Search in Google Scholar

Visscher, F., Bieberle, A., Schubert, M., van der Schaaf, J., de Croon, M., Hampel, U., and Schouten, J. (2012). Water and n-heptane volume fractions in a rotor-stator spinning disc reactor. Ind. Eng. Chem. Res. 51: 16670–16676, https://doi.org/10.1021/ie301439s.Search in Google Scholar

Wei, Q., Leblon, B., and La Rocque, A. (2011). On the use of X-ray computed tomography for determining wood properties: a review. Can. J. For. Res. 41: 2120–2140, https://doi.org/10.1139/x11-111.Search in Google Scholar

Yoshihara, H. and Tsunematsu, S. (2007). Bending and shear properties of compressed Sitka spruce. Wood Sci. Technol. 41: 117–131, https://doi.org/10.1007/s00226-006-0091-8.Search in Google Scholar

Zink, A.G., Davidson, R.W., and Hanna, R.B. (1995). Strain measurement in wood using a digital image correlation technique. Wood Fiber Sci. 27: 346–359.Search in Google Scholar

Received: 2020-04-20
Accepted: 2020-12-03
Published Online: 2021-01-08
Published in Print: 2021-08-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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