Creating Representative Volume Element
by LAMMPS for Finite Element Analysis
Hideyo YOSHIDA, Maiko WATANABE

Background• To evaluate the properties of the Representative Volume Element (RVE),
highly filled with fillers are often needed.
• However, creating such highly filled structure, e.g., filled around 50 vol.%,
by modeling tools for FEM may not be easy.
• By using Molecular Dynamics, It is possible to create these models easily.

Purpose• How high filling is possible ?
• How to create a target filling rate and target shapes ?

Types of Fiber
Create fiber models using 3 types of filler of different thickness and length.
Fiber Name Length Radius Num.
of Fiber of Fiber of BeadForce Field Parameters for MD
LJsigma

LJ
epsilonBond(Harmonic)

Angle(Cosine)

A: L10R1.0

10

1.0

10

2.0

1.0

R0=1.0
K=200

Theta0=180
K=10,000

B: L10R0.5

100.5

20

1.01.0

C: L05R0.5

50.5

101.0

1.0

R0=0.5K=200
R0=0.5
K=200

Theta0=180
K=10,000
Theta0=180
K=10,000

A

L05, R0.5

L10, R0.5

L10, R1.0BCProcess to Create RVE ModelParticle Generation
by COGNAC

Short Relaxation
with Soft Angle

Positioning by Random
Molecular Dynamics
by LAMMPS
Relaxation with Hard Angle

Parameters for MD Calculation
Particle Generation& Short Relaxation
Delta Time
Total Step
Temperature
Angle Potential

Cognac (OCTA)
0.006
10,0001.0
K=500 (Soft)Calculation Time1 ~ 15 [min]Molecular Dynamics
Delta Time
Total Step
Temperature
Angle Potential

LAMMPS
0.001
500,000
1.0e-3
K=10000 (Hard)

Calculation Time3 ~ 50 [min]・Angle Potential
To keep a linear shape of fiber,
it is necessary to set a largevalue as a spring constant of
the angle potential.
・Temperature
To keep linear shape of fiber,temperature is also important.
Sometimes it is effective tolower temperature.

Fiber Shapes of MD Results

System Size
Volume30 x 30 x 30
27,000VF = 0.291

A: L10R1.0 x 250

B: L10R0.5 x 1000

C: L05R0.5 x 2000

A: L10R1.0 x 450

B: L10R0.5 x 1800

C: L05R0.5 x 3600

VF = 0.523

If lowly filled, the fiber shape is kept linear even if length=10.
If highly filled, it is difficult to keep fiber shape. If length=5, the shapes can be kept.

(In this model, even if highly filled and length=10, the shape can be kept by calculating for a longer time at higher temperature.)Creating Mesh Model for FEM

Results of LAMMPS

Getting Densities
by COGNAC

Surface of Fiber

Voxel Meshingby J-OCTA

Voxel Mesh Model for FEM

Target Volume Fraction : 29 %Density Field (Red: Fiber, Blue: Void)& Surface of Filer (Isosurface value = 0.5)
Num. of Grid for getting density = 1,000,000

Voxel Mesh for FEM
Num. of Mesh = 1,000,000

VF = 31.6%

VF = 30.9%

Target Volume Fraction : 52 %Density Field (Red: Fiber, Blue: Void)& Surface of Filer (Isosurface value = 0.5)
Num. of Grid for getting density = 1,000,000

Voxel Mesh for FEM
Num. of Mesh = 1,000,000

VF = 47.3%

VF = 46.2%

Effect of Number of Meshes (Target VF = 52.3%)
Num. of Mesh = 27,000(30 x 30 x 30)* Red: Fiber, Blue: void

Num. of Mesh = 216,000(60 x 60 x 60)

Num. of Mesh = 1,000,000(100 x 100 x 100)

VF = 47.3%

VF = 47.3%

Rad = 1.0

VF = 47.5%Rad = 0.5

VF = 94.9%

NGVF = 46.2%
VF = 46.2%
When the number of meshes is small, the fiber connection may not be expressed.
When Rad = 0.5, at least, mesh number of at least 60 (1 mesh size = 0.5) on a side is required.

Summary
1. By using molecular dynamics,
the highly filled structure models could be created easily.
2. There are a few notes,
 Key Parameters for MD• Potential Parameters of Angle• Temperature and Delta Time Number of Meshes
The number of meshes that can express the particle radius (fiber radius)
is required.
3. Future work
In case of highly filled, the accuracy of density distribution is important.
The method for getting more accurate density distribution and grid size
will be investigated.
Reference[1] http://octa.jp[2] http://www.j-octa.com