Skip to main content
Log in

Numerical modelling of timber and timber joints: computational aspects

  • Original
  • Published:
Wood Science and Technology Aims and scope Submit manuscript

Abstract

Timber joints with their simultaneous ductile and brittle failure modes still pose a major challenge when it comes to modelling. Wood is heterogeneous and highly anisotropic. It shows ductile behaviour in compression and brittle behaviour in tension and shear. A 3D constitutive model for wood based on continuum damage mechanics was developed and implemented via a subroutine into a standard FE framework. Embedment and joint tests using three different wood species (spruce, beech and azobé) were carried out, and the results were compared with modelling outcomes. The failure modes could be identified, and the general shape of the load–displacement curves agreed with the experimental outcomes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

E L :

Modulus of elasticity in longitudinal direction (parallel to the fibre direction)

E R :

Modulus of elasticity in radial direction (perpendicular to the fibre direction)

E T :

Modulus of elasticity in tangential direction (perpendicular to the fibre direction)

G LR :

Shear modulus in LR-plane

G LT :

Shear modulus in LT-plane

G RT :

Shear modulus in RT-plane

f t,0 :

Tensile strength parallel to the fibre direction

f c,0 :

Compressive strength parallel to the fibre direction

f t,90 :

Tensile strength perpendicular to the fibre direction

f c,90 :

Compressive strength perpendicular to the fibre direction

f v :

Shear strength

f roll :

Rolling shear strength

G f,0 :

Fracture energy for tension parallel to the fibre direction

G f,90 :

Fracture energy for tension perpendicular to the fibre direction

G f,v :

Fracture energy for shear

G f,roll :

Fracture energy for rolling shear

d t,0 :

Damage in tension parallel to the fibre direction

d c,0 :

Damage in compression parallel to the fibre direction

d t,90R :

Damage in tension perpendicular to the fibre direction (LT-plane)

d c,90R :

Damage in compression perpendicular to the fibre direction (radial direction)

d t,90T :

Damage in tension perpendicular to the fibre direction (LR-plane)

d c,90T :

Damage in compression perpendicular to the fibre direction (tangential direction)

d vR :

Damage in longitudinal shear (LT-plane)

d vT :

Damage in longitudinal shear (LR-plane)

d roll :

Damage in rolling shear (RT-plane)

σ ij :

Vector of stresses

ε ij :

Vector of strains

D ijkl :

Modified stiffness matrix (including damage)

ν ij :

Poisson ratios

η :

Viscosity parameter

CDM:

Continuum damage mechanics

hss:

High-strength steel

vhss:

Very high-strength steel

C3D8:

3D linear hexahedral elements with 8 nodes

C3D20:

3D quadratic hexahedral elements with 20 nodes

C3D20R:

3D quadratic hexahedral elements with 20 nodes and reduced integration

SDV11:

State variable, showing the damage variable dc,0 in compression parallel to the fibre direction

SDV14:

State variable, showing the damage variable dt,90 in tension perpendicular to the fibre direction

SDV16:

State variable, showing the damage variable dvR in longitudinal shear

COV:

Coefficient of variation

References

  • Ballerini M, Rizzi M (2005) A numerical investigation on the splitting strength of beams loaded perpendicular-to-grain by multiple dowel-type connections. Paper 38-7-1. CIB-W18 Meeting 38, Karlsruhe, Germany

  • Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Matériaux Constr 16(3):155–177. https://doi.org/10.1007/BF02486267

    Article  Google Scholar 

  • Blaß HJ, Bejtka I (2008) Numerische Berechnung der Tragfähigkeit und der Steifigkeit von querzugverstärkten Verbindungen mit stiftförmigen Verbindungsmitteln (Numerical calculation of load-carrying capacity and stiffness of reinforced joints with dowel-type fasteners). Karlsruher Berichte zum Ingenieurholzbau, vol 10. Karlsruhe University of Technology, Germany (in German)

  • Bocquet JF (1997) Modélisation des deformations locales du bois dans les assemblages brochés et boulonnés (Modelling of local deformations of the timber in dowelled and bolted joints). Dissertation, University Blaise Pascal Clermont-Ferrand (in French)

  • Campilho RDSG, de Moura MFSF, Barreto AMJP, Morais JJL, Domingues JJMS (2009) Fracture behaviour of damaged wood beams repaired with an adhesively-bonded composite patch. Compos A 40(6-7):852–859

    Article  Google Scholar 

  • Cofer WF, Du Y, Hermanson JC (1999) Development of a simple three dimensional constitutive model for the analysis of wood, vol 231. American Society of Mechanical Engineers, Applied Mechanics Division (AMD), Mechanics of Cellulosic Materials, New York, pp 107–124

    Google Scholar 

  • Dias AMPG, Van de Kuilen JWG, Cruz HMP, Lopes SMR (2010) Numerical modelling of the load-deformation behavior of doweled softwood and hardwood joints. Wood Fiber Sci 42(4):480–489

    CAS  Google Scholar 

  • Dorn M (2012) Investigations on the serviceability limit state of dowel-type timber connections. Dissertation, Technische Universität Wien

  • Eberhardsteiner J (2002) Mechanisches Verhalten von Fichtenholz; experimentelle Bestimmung der biaxialen Festigkeitseigenschaften (Mechanical behaviour of spruce; experimental determination of biaxial strength properties). Springer, Vienna. ISBN: 978-3-211-83763-4. https://doi.org/10.1007/978-3-7091-6111-1(in German)

    Book  Google Scholar 

  • EN 26891 (1991) Timber structures—joints made with mechanical fasteners—general principles for the determination of strength and deformation characteristics (ISO 6891). Comité Européen de Normalisation (CEN), Brussels

    Google Scholar 

  • EN 338 (2009) Structural timber—strength classes. Comité Européen de Normalisation (CEN), Brussels

    Google Scholar 

  • Federal Highway Administration (2007) Manual for LS-Dyna wood material model 143. Publication No. FHWA-HRT-04-097. U.S. Department of Transportation

  • Fleischmann M (2005) Numerische Berechnung von Holzkonstruktionen unter Verwendung eines realitätsnahen orthotropen elasto-plastischen Werkstoffmodells (Numerical calculations of timber structures using a realistic orthotropic elasto-plastic material model). Dissertation, Technical University, Vienna (in German)

  • Franke S (2008) Zur Beschreibung des Tragverhaltens von Holz unter Verwendung eines photogrammetrischen Messsystems (Description of load-carrying behaviour of timber using a photogrammetric measuring system). Dissertation, Bauhaus University Weimar (in German)

  • Gharib M, Hassanieh A, Valipour H, Bradford MA (2017) Three-dimensional constitutive modelling of arbitrarily orientated timber based on continuum damage mechanics. Finite Elem Anal Des 135:79–90. https://doi.org/10.1016/j.finel.2017.07.008

    Article  Google Scholar 

  • Grosse M (2005) Zur numerischen Simulation des physikalisch nichtlinearen Kurzzeittragverhaltens von Nadelholz am Beispiel von Holz-Beton-Verbundkonstruktionen (Numerical simulation of physical non-linear short-term behaviour of softwood using the example of timber-concrete composite structures). Dissertation, Bauhaus University Weimar (in German)

  • Hambli R (2013) A quasi-brittle continuum damage finite element model of the human proximal femur based on element deletion. Med Biol Eng Comput 51(1–2):219–231. https://doi.org/10.1007/s11517-012-0986-5

    Article  PubMed  Google Scholar 

  • Hashin Z (1980) Failure criteria for unidirectional fiber composites. J Appl Mech Trans ASME 47(2):329–334. https://doi.org/10.1115/1.3153664

    Article  Google Scholar 

  • Hemmer K (1985) Versagensarten des Holzes der Weißtanne (Abies alba) unter mehrachsiger Beanspruchung (Failure modes of fir (Abies alba) subjected to multiaxial loading). Dissertation, University of Technology Karlsruhe (in German)

  • Hofstetter K, Hellmich C, Eberhardsteiner J (2005) Development and experimental validation of a continuum micromechanics model for the elasticity of wood. Eur J Mech A Solids 24(6):1030–1053. https://doi.org/10.1016/j.euromechsol.2005.05.006

    Article  Google Scholar 

  • Jockwer R (2014) Structural behaviour of glued laminated timber beams with unreinforced and reinforced notches. Dissertation, ETH Zürich

  • Juhasz TJ (2003) Ein neues physikalisch basiertes Versagenskriterium für schwach 3D-verstärkte Faserverbundlaminate (A new physical failure criterion for slightly 3D-reinforced composite materials). Dissertation, Technical University Braunschweig (in German)

  • Keenan FJ (1973) Shear strength of glued-laminated timber beams. Dissertation, University of Toronto

  • Khelifa M, Khennane A, El Ganaoui M, Celzard A (2016) Numerical damage prediction in dowel connections of wooden structures. Mater Struct 49:1829–1840. https://doi.org/10.1617/s11527-015-0615-5

    Article  CAS  Google Scholar 

  • Khennane A, Khelifa M, Bleron L, Viguier J (2014) Numerical modelling of ductile damage evolution in tensile and bending tests of timber structures. Mech Mater 68:228–236. https://doi.org/10.1016/j.mechmat.2013.09.004

    Article  Google Scholar 

  • Lee H (2015) Damage modelling for composite structures. Dissertation, University of Manchester

  • Li M, Füssl J, Lukacevic M, Eberhardsteiner J, Martin CM (2018) Strength predictions of clear wood at multiple scales using numerical limit analysis approaches. Comput Struct 196:200–216. https://doi.org/10.1016/j.compstruc.2017.11.005

    Article  Google Scholar 

  • Lopes CS (2009) Damage and failure of non-conventional composite laminates. Dissertation, Delft University of Technology

  • Maimí P (2006) Modelización constitutiva y computacional del daño y la fractura de materiales compuestos (Constitutive numerical modelling of damage and fracture of composite materials). Dissertation, University of Girona (in Spanish)

  • Maimí P, Mayugo JA, Camanho PP (2008) A three-dimensional damage model for transversely isotropic composite laminates. J Compos Mater 42(25):2717–2745. https://doi.org/10.1177/0021998308094965

    Article  CAS  Google Scholar 

  • Maquer G, Schwiedrzik J, Zysset PK (2014) Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression. Comput Methods Biomech Biomed Eng 17(12):1311–1322. https://doi.org/10.1080/10255842.2012.744400

    Article  Google Scholar 

  • Matzenmiller A, Lubliner J, Taylor RL (1995) A constitutive model for anisotropic damage in fiber-composites. Mech Mater 20(2):125–152. https://doi.org/10.1016/0167-6636(94)00053-0

    Article  Google Scholar 

  • Moses DM, Prion HGL (2004) Stress and failure analysis of wood composites: a new model. Compos B Eng 35(3):251–261. https://doi.org/10.1016/j.compositesb.2003.10.002

    Article  Google Scholar 

  • Nagy E, Landis EN, Davids WG (2010) Acoustic emission measurements and lattice simulations of microfracture events in spruce. Holzforschung 64(4):455–461. https://doi.org/10.1515/hf.2010.088

    Article  CAS  Google Scholar 

  • Pinho ST, Dávila CG, Camanho PP, Iannucci L, Robinson P (2005) Failure modes and criteria for FRP under in-plane or three-dimensional stress states including shear non-linearity. Technical Report NASA/TM-2005-213530. NASA Langley Research Center, Hampton, VA, USA

  • Pistoia W, van Rietbergen B, Lochmüller E-M, Lill CA, Eckstein E, Rüegsegger P (2002) Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone 30(6):842–848. https://doi.org/10.1016/S8756-3282(02)00736-6

    Article  CAS  PubMed  Google Scholar 

  • Resch E, Kaliske M (2010) Three-dimensional numerical analyses of load-bearing behavior and failure of multiple double-shear dowel-type connections in timber engineering. Comput Struct 88(3–4):165–177. https://doi.org/10.1016/j.compstruc.2009.09.002

    Article  Google Scholar 

  • Riks E (1972) The application of Newton’s method to the problem of elastic stability. J Appl Mech 39:1060–1066

    Article  Google Scholar 

  • Ruffoni D, van Lenthe GH (2017) 3.10 Finite element analysis in bone research: a computational method relating structure to mechanical function. In: Ducheyne P (ed) Comprehensive Biomaterials II, vol 3. Elsevier, Oxford, pp 169–196

    Chapter  Google Scholar 

  • Saavedra Flores EI, Saavedra K, Hinojosa J, Chandra Y, Das R (2016) Multi-scale modelling of rolling shear failure in cross-laminated timber structures by homogenisation and cohesive zone models. Int J Solids Struct 81:219–232. https://doi.org/10.1016/j.ijsolstr.2015.11.027

    Article  Google Scholar 

  • Sandhaas C (2011) 3D material model for wood, based on continuum damage mechanics. Stevinrapport 6-11-4, Stevin II Laboratory. Delft University of Technology, The Netherlands

  • Sandhaas C (2012) Mechanical behaviour of timber joints with slotted-in steel plates. Dissertation, Delft University of Technology

  • Sandhaas C, Ravenshorst G, Blaß HJ, Van de Kuilen JWG (2013) Embedment tests parallel-to-grain and ductility aspects using various wood species. Eur J Wood Prod 71(5):599–608. https://doi.org/10.1007/s00107-013-0718-z

    Article  CAS  Google Scholar 

  • Schlangen E, Qian Z (2009) 3D modeling of fracture in cement-based materials. J Multiscale Model 1(2):245–261. https://doi.org/10.1142/S1756973709000116

    Article  Google Scholar 

  • Schmid M (2002) Anwendung der Bruchmechanik auf Verbindungen mit Holz (Application of fracture mechanics to timber joints). Dissertation, University of Technology Karlsruhe (in German)

  • Schweigler M, Bader TK, Hochreiner G, Unger G, Eberhardsteiner J (2016) Load-to-grain angle dependence of the embedment behavior of dowel-type fasteners in laminated veneer lumber. Constr Build Mater 126:1020–1033. https://doi.org/10.1016/j.conbuildmat.2016.09.051

    Article  Google Scholar 

  • Sirumbal-Zapata LF, Málaga-Chuquitaype C, Elghazouli AY (2018) A three-dimensional plasticity-damage constitutive model for timber under cyclic loads. Comput Struct 195:47–63. https://doi.org/10.1016/j.compstruc.2017.09.010

    Article  Google Scholar 

  • Spengler R (1982) Festigkeitsverhalten von Brettschichtholz unter zweiachsiger Beanspruchung; Teil 1: Ermittlung des Festigkeitsverhaltens von Brettelementen aus Fichte durch Versuche (Load-carrying behaviour of glued laminated timber subjected to biaxial loading; part 1: experimental determination of load-carrying behaviour of spruce laminations). SFB96, Volume 62, reports on reliability theory of structures. Technical University Munich (in German)

  • Toussaint P (2009) Application et modélisation du principe de la précontrainte sur des assemblages de structure bois. (Application and modelling of the principle of pre-stressing on timber joints). Dissertation, University Henri Poincaré ENSTIB Nancy (in French)

  • Valipour H, Khorsandnia N, Crews K, Foster S (2014) A simple strategy for constitutive modelling of timber. Constr Build Mater 53:138–148. https://doi.org/10.1016/j.conbuildmat.2013.11.100

    Article  Google Scholar 

  • van de Kuilen JWG, Gard W, Ravenshorst G, Antonelli V, Kovryga A (2017) Shear strength values for soft- and hardwoods. Paper 50-6-1. INTER Meeting 50, Kyoto, Japan, pp 49–64

  • Xu BH, Taazount M, Bouchaïr A, Racher P (2009) Numerical 3D finite element modelling and experimental tests for dowel-type timber joints. Constr Build Mater 23(9):3043–3052. https://doi.org/10.1016/j.conbuildmat.2009.04.006

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carmen Sandhaas.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sandhaas, C., Sarnaghi, A.K. & van de Kuilen, JW. Numerical modelling of timber and timber joints: computational aspects. Wood Sci Technol 54, 31–61 (2020). https://doi.org/10.1007/s00226-019-01142-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00226-019-01142-8

Navigation