Prof. Yu's Research Group in the Cloud

Viscoelastic Homogenization with Time-dependent Constituent Properties

This tutorial shows how to calculate cross-sectional properties of the Lenticular boom with given dimensions and material properties using SwiftComp 1.3 and SwiftComp Abaqus GUI.
(Image(l16.PNG) failed - File not found) Flattened height: 45 mm, Web height(one side): 3 mm, Subtended angle: 90 degree, Ply thickness: 0.04 mm, Radius of the flange (curved part): 6.21 mm, Layup: (30)2 . The layup sequence is along with the direction pointing to the center of flange. In this example, we want to compute the effective properties of a composite material made of isotropic viscoelastic matrix and transversely isotropic elastic fiber. The fiber properties are defined by means of engineering constants as specified in the table below.

Fiber properties defined as transversely isotropic elastic

The matrix properties are given as a time-dependent properties, which means that for each time a value of the Young’s modulus is given. In addition, we will consider that the matrix has a constant Poisson’s ratio equal to 0.37. We will create a text file to input the time-dependent material properties as follows.

Time-dependent matrix properties

Please note that for different viscoelastic anisotropies, the material properties should be defined as follows in different columns.

- Transversely isotropic. —- Young’s Modulus, E (t) —- Poisson’s ratio, nu (t) —- Time, t

- Orthotropic defined by means of engineering constants. —- E₁ (t) —- E₂ (t) —- E₃ (t) —- nu₁₂ (t) —- nu₁₃ (t) —- nu₂₃ (t) —- G₁₂ (t) —- G₁₃ (t) —- G₂₃ (t) —- Time, t

- Orthotropic defined by means of stiffness matrix. —- D₁₁₁₁ (t) —- D₁₁₂₂ (t) —- D₂₂₂₂ (t) —- D₁₁₃₃ (t) —- D₂₂₃₃ (t) —- D₃₃₃₃ (t) —- D₁₂₁₂ (t) —- D₁₃₁₃ (t) —- D₂₃₂₃ (t) —- Time, t

- Anisotropic. —- D₁₁₁₁ (t) —- D₁₁₂₂ (t) —- D₂₂₂₂ (t) —- D₁₁₃₃ (t) —- D₂₂₃₃ (t) —- D₃₃₃₃ (t) —- D₁₁₁₂ (t) —- D₂₂₁₂ (t) —- D₃₃₁₂ (t) —- D₁₂₁₂ (t) —- D₁₁₁₃ (t) —- D₂₂₁₃ (t) —- D₃₃₁₃ (t) —- D₁₂₁₃ (t) —- D₁₃₁₃ (t) —- D₁₁₂₃ (t) —- D₂₂₂₃ (t) —- D₃₃₂₃ (t) —- D₁₂₂₃ (t) —- D₁₃₂₃ (t) —— D₂₃₂₃ (t) — Time, t

We will use a square pack 2D SG with fiber volume fraction equal to v_f = 0.64.

Software Used

In his tutorial we will use Abaqus CAE with the Abaqus SwiftComp GUI plug-in. Abaqus CAE will be used to GUI to define the time-dependent material properties and to run the viscoelastic homogenization. SwiftComp will run in the background.

Solution Procedure

The steps required to compute the effective viscoelastic properties using Abaqus SwiftComp GUI are as follows.

# Step 1. We define the material properties in global coordinate system. We click on Materials in Abaqus CAE and define the Fiber properties by means of the engineering constants and click “Ok”.

Definition of the fiber properties

# Step 2. Within the Materials of Abaqus CAE, we create a dummy material called “Matrix”. Please note that we will not define the Prony coefficients of the resin using the Abaqus SwiftComp GUI in the next step.

Creation of the dummy material for the matrix

# Step 3. In the Abaqus SwiftComp GUI menu, we click on Input Time-Dependent Properties. We select “Time-dependent” and “Viscoelastic” in the Method & Analysis section. We pick “Matrix” as the Material to be modified in the drop down menu. Then, we look for the text file used to input the material properties. This text file can be located in any folder of the computer. Finally, we click the two “Ok“s as shown in the picture.

Definition of the matrix Prony coefficients

# Step 4. From the default the Abaqus SwiftComp GUI SGs, we pick the 2D Structure Genome with Square pack. We input the fiber volume fraction, define the approximate global mesh size, and click “Ok”. A square pack microstructure will be automatically generated.

Definition of the 2D SG square pack microstructure

2D SG square pack microstructure

# Step 5. Now, we will compute the effective viscoelastic properties. To do so, we click on Homogenization and select Viscoelastic in Analysis Type. In the Viscoelastic/Thermoviscoelastic Analysis section, we define the range of the time (i.e. Initial time” and Final time”) in which we want to output the effective properties as well as the frequency (i.e. Time increment” defined in decades).

Definition of the viscoelastic homogenization step

# Step 6. We click on Ok to run the homogenization step. SwiftComp on the background will run the homogenization.

SwiftComp running on the background

# Step 7.The results can be found in the .sc.k file as shown next. Note that the effective properties will be outputted for each specified time.

Results corresponding to the effective viscoelastic properties

1. Step 8 .We move on to macroscopic homogenization of the Lenticular boom.

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# Step 9.’Create the part geometry for the Lenticular Boom. Use Set sketch plane for customized SG (Pointed by the Black arrow) -> Use create planar shell -> Select the plane and vertical axis -> Sketch a fourth of the base line (Highlighted as a red line). Its geometry is a straight line (Web height) from (0,12.42) to (0,15.42) and two curved lines (Flange) one from (0,12.42) to (6.21,6.21) centered at (6.21,12.42) and another from (6.21,6.21) to (12.42,0) centered at (6.21,0). Set its thickness to 0.2 mm to the right of the baseline and partition the flange curves at 10° intervals to obtain a smooth curve. Partition the part in the middle to obtain two plies off thickness 0.1 mm each. Mirror the part about the vertical and the horizontal to get the geometry of the Lenticular Boom.
Layups

sketch plane
# Step 10.To enter the material properties for the part, first we need to manually calculate the material properties for both the plies one with orientation 45° and the other with orientation -45°. Choose the material properties from the results of the computed effective viscoelastic properties in the previous section for the appropriate time interval(As required) .Use the formula C’=Rsigma*C*(Rsigma)Transpose to obtain the rotated properties. Now we proceed to enter the properties of the part as follows. Go to Property -> Create material -> Mechanical -> Elasticity -> Elastic -> choose in Type Engineering constants and add the material properties for one of the plies. Repeat the steps for the other ply. Now create two shell homogeneous sections, each one corresponding to one of the materials using the create section option. Now assign the material properties using the assign section option as follows. Select the plies corresponding to the material to select the appropriate section after choosing done.
Material properties

# Step 11. Module > Mesh > Seed Part and choose mesh size, then Click ‘Mesh Part’
Mesh
# Step 12. Homogenize the part to get the final results.
Homogenization

References

1. Liu, X.; Tang, T.; Yu, W., Pipes, R. B.: “Multiscale modeling of viscoelastic behavior of textile composites,” International Journal of Engineering Science, Vol 130, September 2018, pp. 175-186, DOI: 10.1016/j.ijengsci.2018.06.003.

1. Rique, O.; Liu, X.; Yu, W., Pipes, R. B.: “Constitutive modeling for time- and temperature-dependent behavior of composites,” Composites Part B: Engineering, Vol 184, March 2020, DOI: 10.1016/j.compositesb.2019.107726.

Created on 31 Mar 2020, Last modified on 17 Jan 2021