3D network simulations of paper structure - Innventia.com

PAPER PHYSICS
Fig 10. Simulated machine-made sample after compression
Fig 6. Fiber network from Fig. 3 after compression
ΔX
ΔX
L
Fig 7. The sample with 50% mixture of softwood and hardwood
pulps
Fig 8. Fiber network with high filler content – an example of
coating simulation
Fig 9. Filler particles distribution in the fiber mat during coating
formation
Fig 11. Tensile test for elastic modulus calculations
Fiber Network Applications
Calculation of Apparent Elastic Modulus
The apparent elastic modulus is calculated the same way
as usually calculated from the physical tensile test. The
sample length should be at least 1.2 times bigger than the
longest fiber in the network, as recommended in Heyden
2000. The example of such sample is presented in Fig 11
(sample length is 5 mm, width is 1 mm). Material of
fibers is isotropic elastic. Mechanical properties of single
fibers of different dry wooden species can be found in
(Bronkhorst 2003; Page et al. 1977; Katz et al 2008).
Before the solution of elastic boundary-value problem,
the network should be analyzed and bonds between fibers
should be set up. A contact couple can be defined only
between two elements which belong to two different
fibers. From one to four links (bonds) may be set up in
one contact couple. The stiffness of each bond is
calculated from the value of contact area (overlapped area
of two contact surfaces) and bonding stiffness,
experimentally found by Thorpe et al. 1976. The average
maximum shear stress reported by Thorpe et al. 1976 and
Perkins 2001, for the holocellulose bond was
corresponding to an average maximum strain
. The bond stiffness parameter is obtained
as
and is equal to the
spring force between each pair of bonding nodes. Fibers
not bonded to other fibers of the network are eliminated
from consideration. To solve the elastic problem, the
kinematic boundary conditions should be applied to the
finite element grid. Prescribed displacements are assigned
to the nodes located on clamped area on the top and the
bottom surfaces from two opposite sides of the sample,
Fig 11.
After solution of elastic problem, nodal displacements
are used for calculation of strain and stress distributions
in finite elements.
Integration of stresses over element’s area in some
sample cross-sections gives average force and average
Nordic Pulp and Paper Research Journal Vol 27 no.2/2012 259