3D network simulations of paper structure - Innventia.com

PAPER PHYSICS 

3D network simulations of paper structure 

S. Lavrykov, S. B. Lindström, K. M. Singh, B. V. Ramarao 

KEYWORDS: Fiber Network, Random, Hand sheet, 

Bending Stiffness, Elasticity, Compression 

SUMMARY: The structure of paper influences its 

properties and simulations of it are necessary to 

understand the impact of fiber and papermaking 

conditions on the sheet properties. 

We show a method to develop a representative structure 

of paper by merging different simulation techniques for 

the forming section and the pressing operation. The 

simulation follows the bending and drape of fibers over 

one another in the final structure and allows estimation of 

sheet properties without recourse to arbitrary bending 

rules or experimental measurements of density and/or 

RBA. 

Fibers are first modeled as jointed beams following the 

fluid mechanics in the forming section. The sheet 

structure obtained from this is representative of the wet 

sheet from the couch. The pressing simulation discretizes 

fibers into a number of solid elements around the lumen. 

Bonding between fibers is simulated using spring 

elements. 

The resulting fiber network was analyzed to determine 

its elastic modulus and deformation under small strains. 

The influence of fiber dimensions, namely fiber lengths, 

widths and thicknesses as well as bond stiffnesses on the 

elasticity of the network are studied. A brief account of 

inclusion of fines, represented by individual cubical 

elements is also shown. 

ADDRESSES OF THE AUTHORS: 

S. Lavrykov (lavrykov@esf.edu) and B. V. Ramarao 

(bvramara@esf.edu): Empire State Paper Research 

Institute, State University of New York ESF, 1 Forestry 

Dr., Syracuse NY, USA 13210. 

S. B. Lindström (stefan.lindstroem@gmail.com): 

Mechanics, IEI, Institute of Technology, Linköping 

University, 583 81 Linköping, Sweden. 

K. M. Singh (kapil.singh@ipaper.com): International 

Paper Co., Corporate Technology Center, 6283 Tri-Ridge 

Blvd., Loveland, OH 45140, USA. 

Corresponding author: B. V. Ramarao 

In order to investigate the impact of varying fiber 

dimensions or other similar properties on paper 

properties, a number of computer based simulations of 

paper forming have been developed in the past. The 

earliest computer simulations were of two dimensional 

paper structures based on dropping straight or curvilinear 

random lines on a flat plane and investigating the 

statistics of the resulting structure (Kallmes, Corte 1960; 

Corte, Kallmes 1962). The next steps of 2D fiber 

networks were calculations of network mechanical 

properties. Reviews of these are found in Deng and 

Dodson, 1994 and by Bronkhorst, 2003. These 2D 

networks of the paper structure are usually obtained by 

placing the centers of fibers either uniformly randomly or 

with different flocculation rules on a rectangular or 

square area. Fiber orientation is adjusted by sampling 

from known distributions. For mechanical applications, 

256 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012 

fibers were considered as beams - usually as simple 

Bernoulli beams (Heyden 2000; Heyden, Gustafsson 

2002) long free span, and using the Timoshenko model 

for short beams (Räisänen et al., 1996; Bronkhorst, 

2003). The fiber material is usually considered as elastic 

(Van den Akker, 1962; Deng, Dodson, 1994; Kahkonen, 

2003; Heyden 2000; Heyden, Gustafsson 2002). Some 

cases of elastic-plastic simulations are described in 

(Ramasubramanian, Perkins, 1987; Räisänen et al., 1996; 

Bronkhorst, 2003). The intersections of fibers are 

considered as connecting bonds which are either rigid or 

flexible, having some finite transitional and torsional 

stiffness. All 2D fibers models are easy to build and 

analyze, but the following issues render their applicability 

of questionable value for paper materials. It is impossible 

to calculate the thickness (and thus the density) of the 

simulated fiber web. Since paper sheet properties are 

strongly dependent on density, this is perhaps the most 

serious limitation of two dimensional models to simulate 

actual paper properties. Also, since most simulations 

assume rigid inter-fiber bonds, the predictions always 

seriously overestimate the sheet’s elastic moduli (Van 

den Akker, 1963). The number of fiber bonds is also 

grossly overestimated, and therefore even in the case of 

flexible bonds, the elastic modulus predictions are much 

higher than real values. Finally, beam theories are not 

accurate for beams with the extremely short free spans 

such as those occurring in paper. 

Another option to generate real fiber structures is 3D 

networking. Methods for creating three-dimensional fiber 

network structures have been proposed by a number of 

authors as discussed in detail by Alava and Niskanen, 

2006. Some of these models can be used for generation of 

networks similar to hand sheets (Nilsen et al., 1998; 

Provatas et al., 2000; Heyden 2000; Heyden, Gustafsson 

2002; Vincent et al., 2009; Vincent et al., 2010), where 

fiber deposition occurs without considering 

hydrodynamic effects. Straight or curvilinear fibers are 

randomly generated inside an arbitrarily chosen volume, 

(Heyden 2000; Heyden, Gustafsson 2002), or generated 

over rectangular base and then deposited independently 

of each other. During deposition the shape of the fibers 

can change. In the KCL-PAKKA model (Niskanen et al., 

1997; Nilsen et al., 1998) fibers do not bend but a relative 

shift of adjacent fiber segments can be provided 

depending on the stiffness of the wet fiber material and 

applied external pressure. In another case (Vincent et al., 

2009; Vincent et al., 2010), fiber bending was modelled 

according to some artificial bending criteria (two 

prescribed bending angles were introduced, and these 

angles were supposed to be dependent on the wood 

species). An important consideration for paper networks 

is that the free fiber length segments are usually small 

such that bending deformations tend to be limited. 

Generations of artificial machine-made paper sheets, 

where fiber deposition was modeled with the influence of 

water movement, were considered in work of Miettinen

PAPER PHYSICS 

et al. 2007; Switzer et al. 2004; Lindström, Uesaka 2008. 

Pulp fibers were modeled as multilink chains of rigid 

cylindrical segments with circular cross-section, 

immersed into Newtonian liquid. Fiber chains can bend 

and twist due to joints between segments. Different cases 

of liquid motion were considered, including simple 

drainage under gravity and external pressure, (see 

Miettinen et al. 2007; Switzer et al. 2004), and complex 

water movement in different sections of roll-blade 

formers, (Lindström, Uesaka 2008; Lindstrom et al., 

2009). These models suffer some disadvantages such as 

the limitations of rigid segments which do not permit the 

same fiber bending, the output networks have low density 

and higher thickness. However, these methods can be 

used for generating pulp webs of low consistency, and 

thus can simulate forming situations corresponding to the 

wet web before the wet pressing section in the paper 

machine. 

The main goal of the present work is to develop a 

numerical approach to build a 3D artificial hand sheet 

and machine sheet fiber networks with prescribed 

thickness and apparent density, consisting of collapsed 

and non-collapsed fibers, fines and fillers. We can take a 

simulated structure made by using multilink chains of 

rigid cylindrical segments as fibers and abstract the 3D 

structure of the formed paper sheet. The abstraction is by 

using the center lines of the fibers and redecorating their 

thicknesses and widths to develop a fiber model with 

prismatic elements comprising the fibers. The fibers are 

also considered to be hollow to allow for the lumens and 

can be compressed in a wet pressing simulation to 

generate a ‘final’ structure. In the following, we will 

describe our method of generating the paper structure and 

show how it is applied to a random ‘handsheet’ structure 

and a realistic, simulated sheet formed using a twin wire 

roll former with blades. The structures are then analyzed 

for their mechanical properties (in this case, the elastic 

modulus). 

Fiber network Generation 

Hand Sheet Formation 

A set of objects is defined for the simulation, which 

includes objects of three types: fibers, fines or fillers. 

These are characterized by their geometrical parameters 

which include length, width and thickness, their 

distributions and type of cross-section i.e. collapsed or 

non-collapsed, as in Fig 1. Fiber type 1a has only one 

finite element in thickness direction. This type was 

usually used to describe fines and fillers. Fiber types 1b 

and 1c have arbitrary number of elements in all three 

directions (length, width, thickness). Non-collapsed fiber 

type 1d has always one element in the thickness of fiber 

wall and arbitrary number of elements in other two 

directions. It is possible to include curl and kink of fibers 

by suitable modifications of these elementary structures, 

although this was not implemented in the current 

simulation. 

The first step of the simulation is to generate an initial 

structure. Handsheet formation can be simulated by 

simply placing fibers (or objects) randomly in space 

(a) 

(c) 

(b) 

(d) 

Fig 1. Configurations of fibers used in the model 

Frequency 

0,45 

0,40 

0,35 

0,30 

0,25 

0,20 

0,15 

0,10 

0,05 

0,00 

Hardwood Pulp 

0,5 0,9 1,4 2,0 2,7 

Fiber length, mm 

Fig 2. Examples of fiber length distributions for softwood and 

hardwood pulps 

according to their distribution in the furnish. An example 

of such distributions for hard wood and soft wood pulps 

are shown in Fig 2. 

The second step is location of centers of objects in Z 

direction. Each new object has Z coordinate taking into 

account all objects already generated and located below 

this particular one. All points of such line have the same 

Z-coordinate. 

The third step is the generation of finite element grid in 

each object according to type of object cross-section and 

its dimensions. The topology of finite elements (shape 

and local numbering of nodes) should correspond to finite 

element software used in the following steps. In our case 

this was the 8-node hexahedron solid element in the LS- 

DYNA Explicit program. 

Nordic Pulp and Paper Research Journal Vol 27 no.2/2012 257

PAPER PHYSICS 

Fig 4. ZD view of simulated sample structure after forming in 

paper machine 

z max 

z 

z caliper 

Fig 3. An example of initial configuration of fiber network (all 

four fiber configurations and filler particles are presented) 

The fourth step is trimming out the part of finite element 

grid outside prescribed sample dimensions. A sample of 

the finite element network generated after the fourth step 

is shown in Fig 3. 

And the fifth, the last step, is the calculation of fiber 

deposition velocities. All points of each particular object 

have the same initial velocity in vertical direction. The 

velocity is calculated from the deposition height and 

deposition time. 

Machine Sheet Formation 

This method of fiber network generation is described in 

detail by Lindström, Uesaka, 2008. Fibers are represented 

as sets of rigid segments connected by joints with bend 

and torsion stiffness. Mass and moment of inertia of 

segments correspond to solid circular cylinders. Initially 

all fibers are generated randomly inside a prescribed 

volume, which is filled by a viscous incompressible fluid. 

The motion of the fluid is governed by the threedimensional 

Navier–Stokes equations. Equations of 

motion of fiber segments includes inertia forces, 

hydrodynamic drag forces from moving liquid and fiberto-fiber 

contact forces. The slurry is running through 

different sections of paper machine, where different 

boundary conditions are applied (Lindström, Uesaka, 

2008; Lindstrom et al., 2009). The final low consistency 

pulp mat is used as initial input data for the network 

compression model. Each circular fiber is replaced by the 

collapsed or non-collapsed fiber, Fig 1, and is divided 

into a set of finite elements. A mechanical material model 

(elastic, elastic-plastic, visco-elastic-plastic) is assigned 

for each particular fiber. The wet fiber flexibility is a 

fiber parameter that has been investigated extensively in 

the past and can be used to determine a representative 

fiber modulus. Since wet fibers are substantially plastic, it 

is necessary to define plasticity parameters in addition to 

the elasticity. Fibers are anisotropic and their deformation 

is considerably complex. However, for an initial 

simulation such as this, we used a simple isotropic 

bilinear elastic-plastic model with the modulus 

determined from the wet fiber flexibility data in the 

literature [Paavilainen, Luner, 1986; Abitz et al., 1985]. 

An example of machine-generated network is shown in 

Fig 4. 

258 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012 

t load t rest t unload 

Fig 5. Upper rigid plate movement history during mat 

compression 

Fiber network Compression 

The simulation of fiber mat compression was performed 

with the explicit finite element method, [see Zhong 1993 

and Hallquist 2005]. We used LS-DYNA, a program for 

Nonlinear Dynamic Analysis of Structures in Three 

Dimensions, Version 971 (Hallquist 2005). The 8 node 

hexahedron elements with three displacements in each 

node were used to represent fiber network. The central 

finite difference scheme was used for the numerical 

integration of the equations of motion. Fiber-to-fiber 

interactions during simulation were calculated from 

balance of nodal inertia forces, external forces, internal 

forces and contact forces. All contact couples were found 

automatically during simulation. (This method of contact 

handling was made possible by using a keyword 

*CONTACT_AUTOMATIC_GENERAL). 

To obtain the fiber mat with prescribed thickness and 

density, the network was compressed between two rigid 

plates. The non-moving plate is located below the 

previously generated fiber network. The moving plate 

with prescribed motion in vertical direction (Fig 5) is 

initially located on the top of the mat. Fiber settling and 

compression are performed during a loading time , 

which was equal to 1-2 ms. A stabilization time is 

need to decrease dynamic effects in the compressed fiber 

mat which was generally set to 1 ms. An unloading time 

is also needed to remove the upper plate and to 

give the fiber mat possibility to expand in thickness 

direction due to internal stresses in fibers. The unloading 

time was 0.1-1.0 ms usually. 

The results of some 3D network simulations are 

presented in Fig 6-9. The initial fibers configuration from 

Fig 3 after compression is shown in Fig 6. A larger scale 

model with about 1500 fiber of the mixture of hardwood 

and softwood pulps is presented in Fig 7. Results of 

simulation of fiber network with high content of mineral 

filler (25% weight fraction) are shown in Fig 8 and 9. A 

layer created by fillers is observed in the pictures. The 

example of machine-made fiber network after 

compression is shown in Fig 10. The colors serve to 

differentiate the fibers in the network. 

t

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 


PAPER PHYSICS 

Elastic Modulus, GPa 

7,0 

6,0 

5,0 

4,0 

3,0 

2,0 

1,0 

Softwood 

Hardwood 

0,0 

0,09 0,11 0,13 0,15 

Caliper, mm 

Fig 12. Elastic modulus of networks of softwood and hardwood 

pulps 


4,0 

3,0 

2,0 

1,0 

0,0 

5,0 7,5 10,0 12,5 15,0 

Fiber Thickness, µm 

Fig 13. Elastic modulus of simulated network as a function of 

fiber thickness 


4,0 

3,0 

2,0 

1,0 

0,0 

10,0 15,0 20,0 25,0 30,0 35,0 40,0 

Fiber Width, µm 

Fig 14. Elastic modulus of simulated network as a function of 

fiber width 


6,0 

5,0 

4,0 

3,0 

2,0 

1,0 

0,0 

0,0 0,3 0,5 0,8 1,0 1,3 1,5 1,8 

Fiber Length, mm 

Fig 15. Influence of bond stiffness on elastic modulus of fiber 

networks 

0.01 

0.05 

0.1 

0.2 

0.3 

0.4 

0.5 


6,00 

5,95 

5,90 

5,85 

5,80 

0,5 1,0 1,5 2,0 2,5 

Sample Length/Max Fiber Length 

Fig 16. Influence of sample length on elastic modulus of 60 gsm 

fiber network (fiber length 2 mm, sheet caliper 0.1 mm) 

stress in the sample. The strain value is equal to ratio of 

prescribed displacement to the length of free span 

(distance between clamps), so the apparent elastic 

modulus is found. Fig 12 shows the elastic modulus for 

sample networks of softwood and hardwood pulps with 

length distributions shown in Fig 2. The modulus is 

shown as a function of sheet caliper corresponding to 

different wet pressing levels. We observe that the 

modulus increases as the caliper is decreased, i.e. the 

sheet is densified by wet pressing to different levels. It 

can also be seen that the softwood fiber network shows 

higher modulus as compared to the hardwood fibers. This 

result clarifies the impact of fiber length on sheet 

modulus. In order to evaluate the influence of some fiber 

parameters including fiber width, fiber thickness and 

bonding stiffness, on apparent tensile elastic modulus of 

fiber mat we conducted more simulations for fiber mats 

with the same basis weight 60 gsm and the same material 

properties. The results are shown in Figs 12-15 and in 

Table 1. 

Fig 13 and Fig 14 show that the elastic modulus 

decreases with increased thickness (evaluated at constant 

caliper). Increasing thickness results in lesser fibers in the 

sheets, resulting in the lower values observed. Fig 15 

shows the influence of the bond stiffness; increased 

stiffness shows increases in the elastic modulus. 

However, the increase quickly saturates and when the 

bond stiffness increases beyond 0.3, gains in the modulus 

are small. 

The size of the network for simulation of the elastic 

properties should be sufficiently large such that the 

effects of singular fibers spanning a large portion of the 

network are minimized. In order to investigate this 

effect, we carried out simulations of the elastic modulus 

with increasing network length (denoted as sample size) 

keeping fiber length a constant. Fig 16 shows the results 

for fibers of length 2mm. The simulation result for the 

elastic modulus is independent of the network size for 

networks greater than 1.5 fiber lengths. Fig 17 shows a 

graph of the wet pressing pressure as a function of mat 

density for an example softwood and hardwood fibers. 

These are representative calculations indicating that for a 

given wet pressing pressure, the softwood sheets are 

more densified than the hardwoods. The calculations 

serve as illustrative cases since the parameters chosen for 

the fibers were arbitrary. 

260 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012

PAPER PHYSICS 

Table 1. Properties of fibers and simulated 60 gsm sheets, 1x2 mm sample (20F represents fines, fiber objects consisting of single 

elements). 

Parameter 

Softwood pulp Mix 1 

Mix 2 

Mix 3 Hardwood pulp 

0HW+100SW 50HW+50SW 64HW+16SW+20F 80HW+20SW 100HW+0SW 

Fiber Length (Avg.), mm 3.0 2.0 1.2 1.4 1.0 

Fiber Width (Avg.), μm 24 24 24 24 24 

Elastic Modulus Fiber, GPa 10 10 10 10 10 

Caliper, μm 100 100 100 100 100 

Number of fibers 612 783 1162 952 1111 

Elastic Modulus of sheet, GPa 6.433 5.920 4.309 4.278 2.959 

Stiffness (mN·m), simulated 0.536 0.493 0.359 0.356 0.246 

Stiffness (mN·m), experiment 

(Lavrykov et al., 2010) 

0.763 0.703 0.693 

Wet Pressing Pressure, MPa 

60,0 

50,0 

40,0 

30,0 

20,0 

10,0 

Softwood 

Hardwood 

0,0 

0,4 0,5 0,6 0,7 0,8 

Density, g/cm 3 

Fig 17. Pressure as a function of mat density 

Table 1 below shows the results of simulations of 60 

gsm sheets composed of a mix of hardwood and 

softwood pulps in different ratios along with a portion of 

the fines. Note that the mixes are shown in number 

fractions (not mass) as is usual for experimental data. The 

simulation results show that the sheet modulus is a strong 

function of the softwood content, increasing in magnitude 

as this increases. An important parameter, the sheet 

stiffness was also evaluated and shown to be a strong 

function of the softwood content in the pulp. The final 

rows in this table present stiffness estimates using the 

simulations as compared to data obtained from 

experiments. It appears that when the elastic modulus of 

the fibers is assumed to be the same, the longer fibers 

yield a higher stiffness value, a trend that corresponded to 

the experimental results. The magnitudes of the 

stiffnesses observed experimentally are much higher than 

the simulation predictions though. The modulus of the 

fibers and other parameters were obtained from published 

values in the literature rather than measurements or 

estimates on the furnish itself. This would account for the 

difference in magnitude of the estimates. 

Simulation of Wet Pressing of Sheets 

The most significant use of simulation is to predict the 

structure of the paper sheets with particular reference to 

their z-dimensions i.e. the caliper or analogously, their 

density. This is not possible with 2D simulations and also 

simplistic constructions allowing the fibers to bend 

according to external rules. The best method of 

simulation is to determine the fiber reaction force during 

compression, the so-called compressive stress and also 

simultaneously track the drag force exerted by the 

moving fluid. This is possible with a particle level 

simulation such as the present one. The fiber 

displacements were simulated using LS-DYNA. At each 

step of pressing, the fiber reaction force was summed and 

used as the total compressive stress borne by the fibrous 

structure. The combination of the drag, translated into 

permeability and the compressive stress was applied to a 

homogenized wet pressing model (Lavrykov et al., 2009) 

to determine the sheet caliper at different values of 

applied pressure. The hydraulic stress was estimated 

using an effective medium type approximation with 

periodic cells, adjusted for local change in porosity. 

These were combined to generate the structure in a timeexplicit 

method. Fillers (or equivalent fines) were 

considered as single discrete elements of approximately 2 

to 4µm in size. This allowed the calculation of the sheet 

caliper and density at given levels of applied pressure and 

the as a result, the sheet structure. 

Discussion 

As was mentioned before, the main objective of this work 

was to provide a new method for the generation of fiber 

networks which can be applicable to numerical solution 

of mechanical problems. This means fibers in an artificial 

mat should consist of set of finite elements connected in 

nodes. During mat formation fibers should not be bent 

only but compressed too taking into account possible 

fiber collapsing. In this situation all previously reported 

methods (Nilsen et al., 1998; Provatas et al., 2000; 

Heyden 2000; Heyden, Gustafsson 2002; Vincent et al., 

2009; Vincent et al., 2010) were found not correspondent 

to our goals. 

To provide a simulation of fibers settling and 

compression the explicit analysis software was used. 

There are several important reasons for using explicit 

analysis instead of the implicit one for solution of this 

type of problems. First, the explicit methods perform this 

analysis much faster. For example, for the sample in Fig 

7, which contains about 2000 fibers with 120,000 

elements and 500,000 nodes, the solution of the static 

elastic problem using the implicit method on a PC 

computer with two Xeon Quad Core 3 GHz processors 

and 24 GB RAM under 64-bit Windows 7 operational 

system requires 4 Hrs. During solution of nonlinear 

elastic-plastic contact problem with large strains and 


PAPER PHYSICS 

displacements similar time is required for each iteration 

at each loading step. At the same time, the total 

computational time for explicit analysis of this particular 

model was only approximately 6 hrs. Of course, the total 

computational time for explicit analysis is highly 

dependent of integration time step which, in turn, is 

dependent of element size and mechanical properties of 

fiber material - wet fiber density, wet fiber Young’s 

elastic modulus and Poisson’s ratio, (Hallquist 2005). 

Using of mass scaling procedure in LS-DYNA (Hallquist 

2005) can significantly reduce computational time, but 

we did not use this option. 

Second, during solution of contact problems with 

implicit methods using commercial finite element 

software systems like Ansys or Abaqus it is necessary to 

define all contact couples in advance. In fiber network 

compression simulations, the fiber movement is 

unpredictable so contact couples are unknown. In the 

same time, an automatic contact search option is exist in 

explicit analysis software LS-DYNA. 

The simulation itself provides a good tool to understand 

the impact of furnish composition and its changes on 

sheet properties. In addition, by matching the technique 

with simulations of the forming section, more complete 

simulations can be constructed which reflect machine 

operating parameters in addition to the stock variables. 

Conclusions 

A comprehensive network simulation of sheet forming 

was conducted. The simulations show the significance of 

using different fiber level descriptions of the forming 

process in the wet end and wet pressing to construct the 

structure. The resulting structures can be used for 

simulating a variety of transport and mechanical 

properties of paper sheets, and in particular, the effects of 

different fiber furnishes and their treatments. This enables 

the optimization of furnish and processing to obtain high 

performance structures. 

Acknowledgements 

We would like to thank the member companies of the 

Empire State Paper Research Associates, SUNY ESF, 

Syracuse NY for partial funding of this work. 

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