Elasto-plastic material model of green beech wood
Source abstract
Abstract
Abstract Physically modelling the mechanical response of a tree by numerical simulation depends on having accurate data on the mechanical properties of green hardwood. Lacking such data, we developed and validated an orthotropic elasto-plastic (E–P) material model, based on the results of experiments performed on European beech (Fagus sylvatica L.) green wood, capable of including both the non-linearity and orthotropic properties of the material. We selected 655 clear samples with the special orthotropic structure of annual rings. All samples were prepared immediately after felling; their moisture content (MC) was 80% on average. The mechanical responses in normal directions and shear are represented by bi-linear stress–strain curves. The E–P model was validated by comparing the force–deflection response of three-point bending of green wood samples in a finite-element method (FEM) simulation (the average relative error was 4.6% for point-wise and 1.7% for integral-wise comparison). The output of this work was a consistent set of material constants for the E–P material model that is now available for the structural analysis of beech wood with MC above to fibre saturation point (FSP), especially green wood, subjected to relatively high loads (such that a plastic deformation appears) and that can very well predict a non-linear response above the proportional limits.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Tree Root and Stability Studies · Wood Treatment and Properties · Forest ecology and management
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (47)
Show source-provided references
1. Spatz HC, Pfisterer J (2013) Mechanical properties of green wood and their relevance for tree risk assessment. Arboric Urban For 39:218–225
2. Klement I, Vilkovský P, Vilkovská T (2022) Change in selected mechanical properties of beech wood at the contact drying. Materials 15(21):7433. https://doi.org/10.3390/ma1521743310.3390/ma15217433 ↗
3. Niklas KJ, Spatz HC (2010) Worldwide correlations of mechanical properties and green wood density. Am J Bot 97:1587–1594. https://doi.org/10.3732/ajb.100015010.3732/ajb.1000150 ↗
4. Wu Y, Shao Z (2016) Measurement and mechanical analysis of the strains-stresses induced by tree-pulling experiments in tree stems. Trees Struct Funct 30:675–684. https://doi.org/10.1007/s00468-015-1310-410.1007/s00468-015-1310-4 ↗
5. Kane B, Clouston P (2008) Tree pulling tests of large shade trees in the genus Acer. Arboric Urban For 34:101–10910.48044/jauf.2008.013 ↗
6. Tippner J, Praus L, Brabec M, Sebera V, Vojáčková B, Milch J (2019) Using 3D digital image correlation in an identification of defects of trees subjected to bending. Urban For Urban Green 46:1–10. https://doi.org/10.1016/j.ufug.2019.12651310.1016/j.ufug.2019.126513 ↗
7. Forest Products Laboratory US (2010) Wood handbook : Wood as an engineering material. Centennial ed, Madison Wis: U.S. Dept. of Agriculture Forest Service Forest Products Laboratory, Madison, Wisconsin
8. Wessolly L, Erb M (2014) Manual of tree statics and tree inspection. Irish For 74.
9. Jackson T, Shenkin A, Wellpott A, Calders K, Origo N, Disney M, Burt A, Raumonen P, Gardiner B, Herold M, Fourcaud T, Malhi Y (2019) Finite element analysis of trees in the wind based on terrestrial laser scanning data. Agric For Meteorol 265:137–144. https://doi.org/10.1016/j.agrformet.2018.11.01410.1016/j.agrformet.2018.11.014 ↗
10. Vojáčková B, Tippner J, Horáček P, Sebera V, Praus L, Mařík R, Brabec M (2021) The effect of stem and root-plate defects on the tree response during static loading—numerical analysis. Urban For Urban Green 59:127002. https://doi.org/10.1016/j.ufug.2021.12700210.1016/j.ufug.2021.127002 ↗
11. Middleton W, Erdal HI, Detter A, D’Acunto P, Ludwig F (2023) Comparing structural models of linear elastic responses to bending in inosculated joints. Trees Struct Funct 37:891–903. https://doi.org/10.1007/s00468-023-02392-710.1007/s00468-023-02392-7 ↗
12. Lundström T, Jonas T, Volkwein A (2008) Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite element model and experimental data. J Exp Bot 59:2513–2528. https://doi.org/10.1093/jxb/ern11610.1093/jxb/ern116 ↗
13. Stubbs CJ, Baban NS, Robertson DJ, Alzube L, Cook DD (2018) Bending stress in plant stems: Models and assumptions. In: Geitmann A, Gril J (eds) Plant Biomechanics. Springer, Cham (10.1007/978-3-319-79099-2_3)
14. Lundström T, Heiz U, Stoffel M, Stockli V (2007) Fresh-wood bending: linking the mechanical and growth properties of a Norway spruce stem. Tree Physiol 27(9):1229–1241. https://doi.org/10.1093/treephys/27.9.122910.1093/treephys/27.9.1229 ↗
15. Evert RF (2006) Xylem: secondary xylem and variations in wood structure. Esaus Plant Anat. https://doi.org/10.1002/0470047380.ch1110.1002/0470047380.ch11 ↗
16. Malaga-Toboła U, Łapka M, Tabor S, Niesłony A, Findura P (2019) Influence of wood anisotropy on its mechanical properties in relation to the scale effect. Int Agrophys 33:337–345. https://doi.org/10.31545/intagr/11080810.31545/intagr/110808 ↗
17. Moses DM, Prion HL (2004) Stress and failure analysis of wood composites: a new model. Compos Part B Eng 35:251–261. https://doi.org/10.1016/j.compositesb.2003.10.00210.1016/j.compositesb.2003.10.002 ↗
18. Oudjene M, Khelifa M (2009) Finite element modelling of wooden structures at large deformations and brittle failure prediction. Mater Des 30:4081–4087. https://doi.org/10.1016/j.matdes.2009.05.02410.1016/j.matdes.2009.05.024 ↗
19. Hong J-P, Lee J-J, Yeo H, Kim C-K, Pang S-J, Oh J-K (2015) Parametric study on the capability of three-dimensional finite element analysis (3D-FEA) of compressive behaviour of Douglas fir. Holzforschung 70(6):539–546. https://doi.org/10.1515/hf-2015-015110.1515/hf-2015-0151 ↗
20. Sohouli AR, Goudarzi AM, Alashti RA (2011) Finite element analysis of elastic-plastic contact mechanic considering the effect of contact geometry and material properties. J Surf Eng Mat Adv Technol 01(03):125–129. https://doi.org/10.4236/jsemat.2011.1301910.4236/jsemat.2011.13019 ↗
21. Mackerle J (2005) Finite element analyses in wood research: a bibliography. Wood Sci Technol 39(7):579–600. https://doi.org/10.1007/s00226-005-0026-910.1007/s00226-005-0026-9 ↗
22. Hill R (1950) The mathematical theory of plasticity. The Oxford Engineering Science Series, Oxford, pp 97–114
23. Milch J, Tippner J, Sebera V, Brabec M (2016) Determination of the elasto-plastic material characteristics of Norway spruce and European beech wood by experimental and numerical analyses. Holzforschung 70:1081–1092. https://doi.org/10.1515/hf-2015-026710.1515/hf-2015-0267 ↗
24. Tippner J, Milch J, Sebera V, Brabec M (2022) Elasto-plastic material model of oak at two moisture content levels. Holzforschung 76:886–896. https://doi.org/10.1515/hf-2022-000810.1515/hf-2022-0008 ↗
25. Bodig J, Jayne B (1982) Mechanics of wood and wood composites, Repr. Krieger, Malabara
26. Clouston PL, Lam F (2002) A stochastic plasticity approach to strength modelling of strand-based wood composites. Compos Sci Technol 62(10–11):1381–1395. https://doi.org/10.1016/S0266-3538(02)00086-610.1016/S0266-3538(02)00086-6 ↗
27. Moses DM, Prion HGL (2002) Anisotropic plasticity and the notched wood shear block. For Prod J 52(6):43–54
28. Yoshihara H (2007) Simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end-notched flexure. Holzforschung 61:182–189. https://doi.org/10.1515/HF.2007.03210.1515/HF.2007.032 ↗
29. Fiorelli J, Dias AA (2006) Fiberglass-reinforced glulam beams: mechanical properties and theoretical model. Mater Res 9:263–269. https://doi.org/10.1590/S1516-1439200600030000410.1590/S1516-14392006000300004 ↗
30. Hering S, Keunecke D, Niemz P (2012) Moisture-dependent orthotropic elasticity of beech wood. Wood Sci Technol 46:927–938. https://doi.org/10.1007/s00226-011-0449-410.1007/s00226-011-0449-4 ↗
31. Hong J-P, Lee J-J, Oh J-K (2014) Elasto-plastic anisotropic wood material model for finite solid element applications. J Korean Wood Sci Technol 42(4):367–375. https://doi.org/10.5658/wood.2014.42.4.36710.5658/wood.2014.42.4.367 ↗
32. Šebek F, Kubík P, Tippner J, Brabec M (2021) Orthotropic elastic-plastic-damage model of beech wood based on split Hopkinson pressure and tensile bar experiments. Int J Impact Eng 157:103975. https://doi.org/10.1016/j.ijimpeng.2021.10397510.1016/j.ijimpeng.2021.103975 ↗
33. Ansys® Mechanical APDL, Release 2020 R2, Help System, ANSYS, Inc.
34. Hearmon, RFS (1948) The elasticity of wood and plywood. Special Report no. 7. HM Stationery Office, London
35. BS 373 (1957) Methods of testing small clear specimens of timber. London: British Standards Institution, London
36. ČSN 49 0110 (1980) Drevo. Medza pevnosti v tlaku v smere vlákien [in Slovak] , Český normalizační institut, Praha
37. ČSN 49 0111 (1992) Skúšky vlastností rastlého dreva. Metóda zisťovania modulu pružnosti v tlaku pozdĺž vlákien [in Slovak], Český normalizační institut, Praha
38. ČSN 49 0112 (1979) Drevo. Tlak naprieč vlákien [in Slovak] , Český normalizační institut, Praha
39. ČSN 49 0118 (1980) Drevo. Medza pevnosti v šmyku v smere vlákien [in Slovak] , Český normalizační institut, Praha
40. ČSN 49 0113 (1992) Skúšky vlastností rastlého dreva. Metóda zisťovania pevnosti v ťahu pozdĺž vlákien [in Slovak] , Český normalizační institut, Praha
41. ČSN 49 0114 (1992) Skúšky vlastností rastlého dreva. Metóda zisťovania pevnosti v ťahu naprieč vlákien [in Slovak] , Český normalizační institut, Praha
42. ČSN 49 0115 (1979) Drevo. Zisťovanie medze pevnosti v statickom ohybe [in Slovak] , Český normalizační institut, Praha
43. Brabec M, Tippner J, Sebera V, Milch J, Rademacher P (2015) Standard and non-standard deformation behaviour of European beech and Norway spruce during compression. Holzforschung 69(9):1107–1116. https://doi.org/10.1515/hf-2014-023110.1515/hf-2014-0231 ↗
44. ČSN 49 0103 (1980). Drevo. Zisťovanie vlhkosti pri fyzikálnych a mechanických skúškach [in Slovak], Český normalizační institut, Praha
45. Bachtiar EV, Rüggeberg M, Hering S, Kaliske M, Niemz P (2017) Estimating shear properties of walnut wood: a combined experimental and theoretical approach. Mater Struct 50:248. https://doi.org/10.1617/s11527-017-1119-210.1617/s11527-017-1119-2 ↗
46. Babiak M, Gaff M, Sikora A, Hysek Š (2018) Modulus of elasticity in three-and four-point bending of wood. Compos Struct 204:454–465. https://doi.org/10.1016/j.compstruct.2018.07.11310.1016/j.compstruct.2018.07.113 ↗
47. Pěnčík J (2015) Tests of wooden specimens from Scots pine (Pinus sylvestris) with the help of anisotropic plasticity material model. Drvna Ind 66:27–33. https://doi.org/10.5552/drind.2015.136210.5552/drind.2015.1362 ↗