Week - 10 Hyperelastic Material Models

Objective:

The aim of this study is to calculate the Mooney Rivlin and Ogden material constants and compare them using stress-strain data obtained from a Dogbone specimen tensile test with 100 percent strain.

Background:

Hyperelastic materials are defined as materials that can undergo more than 100% strain without experiencing failure. These materials are challenging to replicate due to their high strain values and typically have a Poisson's ratio close to 0.5. Various material models such as Mooney Rivlin, Ogden, and Yeoh are commonly used to describe the behavior of these materials. These models define the materials using strain energy versus stretch relationships, with strain energy represented by the area under the stress-strain curve. In this study, we will focus on modeling the Mooney Rivlin and Ogden materials using the provided stress-strain data.

PROCEDURE:

1. Create the given data in excel file.

plot

2. Import the dogbone specimen in Ls Dyna.

Mooney Rivlin Material

• Now from Experimental data Image we will input the given data into Excel and input the same data in the curve data of LS-DYNA.
• Now we will go to the Define>>curve and input the value of curve data to get the curve.
  

• create section card from keyword>>all>>section>>shell>>here we will input id, elform type

• Now we will create the MAT card for it as MAT_HYPERELASTIC_RUBBER (MAT_077_H).

• Initially we will start with N=1, then N=3 and calculate the stress and stretch ratio and then calculate the engg. stress and strain and also we will get the values of constants, C10, C01 and other constants.

• Assign the section and material to the part.

• Constrain all the nodes of one end of the dog bone specimen in all directions except translational Y direction.

• Constrain the mid nodes of both ends of the dog bone specimen in Y translation to restrict the slip during simulation.

• Assign Displacement for the specimen onset of nodes on another side with the curve defined.

• Now we have to create the control cards for finalisation of output.
• Now we will create the control_ternimation card.

• create Control Implicit General, Control Implicit Auto & Control Implicit Solver.

• BINARY_D3PLOT -  It defines the frequency at which the animation file is to be created and is set to 0.1ms.

• Extent Bianry database card.

• The output request in ASCII format, The following keyword are activated

1. ELOUT-Element Output Data
2. GLSTAT- Global Data
3. MATSUM- Material Energies and
4. RCFORC: Resultant Interface Forces

check the model and then head for simulation

Analysis setup for Curve Fit:-

1.For N=1

1. Save the Keyword and run the Model In Ls Dyna manager

2. Open the d3hsp File in Notepad++ for Mooney Rivlin COnstants

3. From The d3hsp file, Mooney Rivlin constants are obtained along with the Stretch and true stress value

C10=0.1768E+00

C01=0.1474E+00

The stretch and True Stress values are converted into Engineering Strain and Engineering stress values 

Stretch is Change in length by original Length which is denoted by $\lambda$

Engineering Strain=$\lambda -1$

Engineering Stress= True stress/1+Engineering Strain

2. For N=2:-

1. Change N=2 from the Material card and Run the simulation again

2. Open the d3hsp File in Notepad++ for Mooney Rivlin COnstants

3. From The d3hsp file, Mooney Rivlin constants are obtained along with the Stretch and true stress values

C10=0.2595000

C01=0.4594E-01

C11=-0.2092E-01

C20=0.2914E-02

C02=0.1016E-02

C30=0.0000E+00

Similarly, the Stretch and True stress values are converted to Engineering Strain and Engineering stress values

3.For N=3:-

Change N=3 from the Material card and Run the simulation again

2. Open the d3hsp File in Notepad++ for Mooney Rivlin Constants

3. From The d3hsp file, Mooney Rivlin constants are obtained along with the Stretch and true stress values

C10=0.2611E+00

C01=0.4420E-01

C11=-0.6074E-02

C20=-0.2667E-02

C02=-0.9968E-02

C30=0.1565E-03

Similarly, the Stretch and True stress values are converted to Engineering Strain and Engineering stress values

As we can see all the Constant values obtained from the d3hsp file is fitting with the Original Data

So from this, we can conclude all the Constants will Give similar results in compared with the original data 

Material Validation:-

Change N=0 in the Material card and input the Mooney Rivlin Constants Individually Obtained from N=1, N=2, N=3 and validate 

Constants from N=1                                                                                                                                                                   Constants From N=2:

 Constants From N=3

The Simulation is Done Individually with The Constants Obtained from N=1, N=2, N=3

The True Stress and Strain Values Obtained from the Element is Converted to Engineering Stress/ strain

The Constants From N=1,2,3 are plotted with original Data 

Conclusion

The results show that the Ogden material is more compressed in this simulation compared to the Hyperelastic material. Both materials exhibit similar properties. The Hyperelastic material provides a more accurate fit compared to the Ogden material, and the fit remains constant for all parameters.