Numerical modelling of timber and timber joints: computational aspects

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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.

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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


Continuum damage mechanics


High-strength steel


Very high-strength steel


3D linear hexahedral elements with 8 nodes


3D quadratic hexahedral elements with 20 nodes


3D quadratic hexahedral elements with 20 nodes and reduced integration


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


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


State variable, showing the damage variable dvR in longitudinal shear


Coefficient of variation


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

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