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Wood Science and Technology

, Volume 54, Issue 1, pp 31–61 | Cite as

Numerical modelling of timber and timber joints: computational aspects

  • Carmen SandhaasEmail author
  • Ani Khaloian Sarnaghi
  • Jan-Willem van de Kuilen
Original
  • 100 Downloads

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.

List of symbols

EL

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

ER

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

ET

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

GLR

Shear modulus in LR-plane

GLT

Shear modulus in LT-plane

GRT

Shear modulus in RT-plane

ft,0

Tensile strength parallel to the fibre direction

fc,0

Compressive strength parallel to the fibre direction

ft,90

Tensile strength perpendicular to the fibre direction

fc,90

Compressive strength perpendicular to the fibre direction

fv

Shear strength

froll

Rolling shear strength

Gf,0

Fracture energy for tension parallel to the fibre direction

Gf,90

Fracture energy for tension perpendicular to the fibre direction

Gf,v

Fracture energy for shear

Gf,roll

Fracture energy for rolling shear

dt,0

Damage in tension parallel to the fibre direction

dc,0

Damage in compression parallel to the fibre direction

dt,90R

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

dc,90R

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

dt,90T

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

dc,90T

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

dvR

Damage in longitudinal shear (LT-plane)

dvT

Damage in longitudinal shear (LR-plane)

droll

Damage in rolling shear (RT-plane)

σij

Vector of stresses

εij

Vector of strains

Dijkl

Modified stiffness matrix (including damage)

νij

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

Notes

Compliance with ethical standards

Conflict of interest

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Timber Structures and Building ConstructionKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Holzforschung MünchenTechnical University MunichMunichGermany
  3. 3.Biobased Structures and MaterialsDelft University of TechnologyDelftThe Netherlands

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