Week - 10 Hyperelastic Material Models
Week - 10 Hyperelastic Material Models
AIM:
To calculate the Mooney Rivlin and Ogden material constants and compare the both using stress-strain data from a Dogbone specimen tensile test with 100 percent strain.
Theory:
- Hyper elastic materials are the material which has the capability to stretch with more than 100 % strain without any sort of failure.
- These material are hard to replicate as the strain value are high. These materials have Poisson’s ratio of almost 0.5.
- Various material models like Mooney Rivlin, Ogden, Yeoh etc are used to model these materials.
- These materials can be defined using strain energy vs stretch relations, where strain energy is the area under stress-strain graph.
- Here we will discuss modelling of Mooney Rivlin and Ogden material using the given stress strain data.
PROCEDURE:
1. Create the given data in excel file.
Data:
| 0 | 0 |
| 2.50E-02 | 4.46E-02 |
| 5.00E-02 | 8.67E-02 |
| 7.50E-02 | 1.27E-01 |
| 1.00E-01 | 1.64E-01 |
| 1.25E-01 | 2.00E-01 |
| 1.50E-01 | 2.34E-01 |
| 1.75E-01 | 2.67E-01 |
| 2.00E-01 | 2.98E-01 |
| 2.25E-01 | 3.28E-01 |
| 2.50E-01 | 3.56E-01 |
| 2.75E-01 | 3.83E-01 |
| 3.00E-01 | 4.09E-01 |
| 3.25E-01 | 4.34E-01 |
| 3.50E-01 | 4.58E-01 |
| 3.75E-01 | 4.81E-01 |
| 4.00E-01 | 5.03E-01 |
| 4.25E-01 | 5.24E-01 |
| 4.50E-01 | 5.45E-01 |
| 4.75E-01 | 5.65E-01 |
| 5.00E-01 | 5.84E-01 |
| 5.25E-01 | 6.03E-01 |
| 5.50E-01 | 6.20E-01 |
| 5.75E-01 | 6.38E-01 |
| 6.00E-01 | 6.55E-01 |
| 6.25E-01 | 6.71E-01 |
| 6.50E-01 | 6.87E-01 |
| 6.75E-01 | 7.02E-01 |
| 7.00E-01 | 7.17E-01 |
| 7.25E-01 | 7.32E-01 |
| 7.50E-01 | 7.46E-01 |
| 7.75E-01 | 7.60E-01 |
| 8.00E-01 | 7.73E-01 |
| 8.25E-01 | 7.86E-01 |
| 8.50E-01 | 7.99E-01 |
| 8.75E-01 | 8.11E-01 |
| 9.00E-01 | 8.23E-01 |
| 9.25E-01 | 8.35E-01 |
| 9.50E-01 | 8.47E-01 |
| 9.75E-01 | 8.58E-01 |
| 1.00E+00 | 8.69E-01 |
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
- ELOUT-Element Output Data
- GLSTAT- Global Data
- MATSUM- Material Energies and
- RCFORC: Resultant Interface Forces
check the model and then head for simulation.
- The d3hsp file for each material model is opened in notepad++ and the material constants of Mooney-Rivlin as well as final fit data of stretch and Engg. stress is obtained for each case.
Mooney Rivlin Material Constant,
From N1
| Mooney constant c1 = | 0.1768 |
| Mooney constant c2 = | 1.47E-01 |
For the Ogden Rubber constant,
Material Card:
- The d3hsp file for each material model is opened in notepad++ and the material constants of Ogden Rubber Constant.
Ogden Rubber Constant,
From N3,
| Hyperelastic Constant C10= | 2.61E-01 |
| Hyperelastic Constant C01= | 4.42E-02 |
| Hyperelastic Constant C11= | -6.07E-03 |
| Hyperelastic Constant C20= | -2.67E-03 |
| Hyperelastic Constant C02= | -9.97E-03 |
| Hyperelastic Constant C30= | 1.57E-04 |
- Now we will calculate the engg. stress and engg. strain values from the calculated values by N=1 & 3.
Engineering Strain = Exp(True strain) - 1
stretch = (1+Engineering strain)
Engineering stress = True stress/(1+Engineering strain)
= True stress/stretch
| Experimental | Mooney-Rivlin material model | Ogden Rubber Constant | |||||||
| Engg strain | Engg stress | Stretch | True stress | Engg Strain | Engg Stress | Stretch | True Stress | Engg Strain | Engg Stress |
| 0 | 0 | 1.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
| 2.50E-02 | 4.46E-02 | 1.03E+00 | 4.81E-02 | 2.50E-02 | 4.69E-02 | 1.03E+00 | 4.56E-02 | 2.50E-02 | 4.45E-02 |
| 5.00E-02 | 8.67E-02 | 1.05E+00 | 9.52E-02 | 5.00E-02 | 9.07E-02 | 1.05E+00 | 9.10E-02 | 5.00E-02 | 8.66E-02 |
| 7.50E-02 | 1.27E-01 | 1.08E+00 | 1.42E-01 | 7.50E-02 | 1.32E-01 | 1.08E+00 | 1.36E-01 | 7.50E-02 | 1.27E-01 |
| 1.00E-01 | 1.64E-01 | 1.10E+00 | 1.87E-01 | 1.00E-01 | 1.70E-01 | 1.10E+00 | 1.81E-01 | 1.00E-01 | 1.64E-01 |
| 1.25E-01 | 2.00E-01 | 1.13E+00 | 2.32E-01 | 1.25E-01 | 2.06E-01 | 1.13E+00 | 2.25E-01 | 1.25E-01 | 2.00E-01 |
| 1.50E-01 | 2.34E-01 | 1.15E+00 | 2.76E-01 | 1.50E-01 | 2.40E-01 | 1.15E+00 | 2.70E-01 | 1.50E-01 | 2.34E-01 |
| 1.75E-01 | 2.67E-01 | 1.18E+00 | 3.20E-01 | 1.75E-01 | 2.72E-01 | 1.18E+00 | 3.14E-01 | 1.75E-01 | 2.67E-01 |
| 2.00E-01 | 2.98E-01 | 1.20E+00 | 3.64E-01 | 2.00E-01 | 3.03E-01 | 1.20E+00 | 3.58E-01 | 2.00E-01 | 2.98E-01 |
| 2.25E-01 | 3.28E-01 | 1.23E+00 | 4.07E-01 | 2.25E-01 | 3.32E-01 | 1.23E+00 | 4.01E-01 | 2.25E-01 | 3.28E-01 |
| 2.50E-01 | 3.56E-01 | 1.25E+00 | 4.49E-01 | 2.50E-01 | 3.60E-01 | 1.25E+00 | 4.45E-01 | 2.50E-01 | 3.56E-01 |
| 2.75E-01 | 3.83E-01 | 1.28E+00 | 4.92E-01 | 2.75E-01 | 3.86E-01 | 1.28E+00 | 4.88E-01 | 2.75E-01 | 3.83E-01 |
| 3.00E-01 | 4.09E-01 | 1.30E+00 | 5.34E-01 | 3.00E-01 | 4.11E-01 | 1.30E+00 | 5.32E-01 | 3.00E-01 | 4.09E-01 |
| 3.25E-01 | 4.34E-01 | 1.33E+00 | 5.77E-01 | 3.25E-01 | 4.35E-01 | 1.33E+00 | 5.75E-01 | 3.25E-01 | 4.34E-01 |
| 3.50E-01 | 4.58E-01 | 1.35E+00 | 6.19E-01 | 3.50E-01 | 4.58E-01 | 1.35E+00 | 6.18E-01 | 3.50E-01 | 4.58E-01 |
| 3.75E-01 | 4.81E-01 | 1.38E+00 | 6.61E-01 | 3.75E-01 | 4.81E-01 | 1.38E+00 | 6.61E-01 | 3.75E-01 | 4.81E-01 |
| 4.00E-01 | 5.03E-01 | 1.40E+00 | 7.03E-01 | 4.00E-01 | 5.02E-01 | 1.40E+00 | 7.04E-01 | 4.00E-01 | 5.03E-01 |
| 4.25E-01 | 5.24E-01 | 1.43E+00 | 7.45E-01 | 4.25E-01 | 5.23E-01 | 1.43E+00 | 7.47E-01 | 4.25E-01 | 5.24E-01 |
| 4.50E-01 | 5.45E-01 | 1.45E+00 | 7.87E-01 | 4.50E-01 | 5.43E-01 | 1.45E+00 | 7.90E-01 | 4.50E-01 | 5.45E-01 |
| 4.75E-01 | 5.65E-01 | 1.48E+00 | 8.29E-01 | 4.75E-01 | 5.62E-01 | 1.48E+00 | 8.33E-01 | 4.75E-01 | 5.65E-01 |
| 5.00E-01 | 5.84E-01 | 1.50E+00 | 8.71E-01 | 5.00E-01 | 5.81E-01 | 1.50E+00 | 8.76E-01 | 5.00E-01 | 5.84E-01 |
| 5.25E-01 | 6.03E-01 | 1.53E+00 | 9.13E-01 | 5.25E-01 | 5.99E-01 | 1.53E+00 | 9.19E-01 | 5.25E-01 | 6.03E-01 |
| 5.50E-01 | 6.20E-01 | 1.55E+00 | 9.56E-01 | 5.50E-01 | 6.17E-01 | 1.55E+00 | 9.62E-01 | 5.50E-01 | 6.21E-01 |
| 5.75E-01 | 6.38E-01 | 1.58E+00 | 9.98E-01 | 5.75E-01 | 6.34E-01 | 1.58E+00 | 1.01E+00 | 5.75E-01 | 6.38E-01 |
| 6.00E-01 | 6.55E-01 | 1.60E+00 | 1.04E+00 | 6.00E-01 | 6.51E-01 | 1.60E+00 | 1.05E+00 | 6.00E-01 | 6.55E-01 |
| 6.25E-01 | 6.71E-01 | 1.63E+00 | 1.08E+00 | 6.25E-01 | 6.67E-01 | 1.63E+00 | 1.09E+00 | 6.25E-01 | 6.71E-01 |
| 6.50E-01 | 6.87E-01 | 1.65E+00 | 1.13E+00 | 6.50E-01 | 6.82E-01 | 1.65E+00 | 1.13E+00 | 6.50E-01 | 6.87E-01 |
| 6.75E-01 | 7.02E-01 | 1.68E+00 | 1.17E+00 | 6.75E-01 | 6.99E-01 | 1.68E+00 | 1.18E+00 | 6.75E-01 | 7.02E-01 |
| 7.00E-01 | 7.17E-01 | 1.70E+00 | 1.21E+00 | 7.00E-01 | 7.14E-01 | 1.70E+00 | 1.22E+00 | 7.00E-01 | 7.17E-01 |
| 7.25E-01 | 7.32E-01 | 1.73E+00 | 1.26E+00 | 7.25E-01 | 7.29E-01 | 1.73E+00 | 1.26E+00 | 7.25E-01 | 7.32E-01 |
| 7.50E-01 | 7.46E-01 | 1.75E+00 | 1.30E+00 | 7.50E-01 | 7.43E-01 | 1.75E+00 | 1.31E+00 | 7.50E-01 | 7.46E-01 |
| 7.75E-01 | 7.60E-01 | 1.78E+00 | 1.35E+00 | 7.75E-01 | 7.58E-01 | 1.78E+00 | 1.35E+00 | 7.75E-01 | 7.59E-01 |
| 8.00E-01 | 7.73E-01 | 1.80E+00 | 1.39E+00 | 8.00E-01 | 7.72E-01 | 1.80E+00 | 1.39E+00 | 8.00E-01 | 7.73E-01 |
| 8.25E-01 | 7.86E-01 | 1.83E+00 | 1.43E+00 | 8.25E-01 | 7.85E-01 | 1.83E+00 | 1.44E+00 | 8.25E-01 | 7.86E-01 |
| 8.50E-01 | 7.99E-01 | 1.85E+00 | 1.48E+00 | 8.50E-01 | 7.99E-01 | 1.85E+00 | 1.48E+00 | 8.50E-01 | 7.99E-01 |
| 8.75E-01 | 8.11E-01 | 1.88E+00 | 1.52E+00 | 8.75E-01 | 8.12E-01 | 1.88E+00 | 1.52E+00 | 8.75E-01 | 8.11E-01 |
| 9.00E-01 | 8.23E-01 | 1.90E+00 | 1.57E+00 | 9.00E-01 | 8.26E-01 | 1.90E+00 | 1.56E+00 | 9.00E-01 | 8.23E-01 |
| 9.25E-01 | 8.35E-01 | 1.93E+00 | 1.61E+00 | 9.25E-01 | 8.38E-01 | 1.93E+00 | 1.61E+00 | 9.25E-01 | 8.35E-01 |
| 9.50E-01 | 8.47E-01 | 1.95E+00 | 1.66E+00 | 9.50E-01 | 8.51E-01 | 1.95E+00 | 1.65E+00 | 9.50E-01 | 8.47E-01 |
| 9.75E-01 | 8.58E-01 | 1.98E+00 | 1.71E+00 | 9.75E-01 | 8.64E-01 | 1.98E+00 | 1.70E+00 | 9.75E-01 | 8.58E-01 |
| 1.00E+00 | 8.69E-01 | 2.00E+00 | 1.75E+00 | 1.00E+00 | 8.77E-01 | 2.00E+00 | 1.74E+00 | 1.00E+00 | 8.69E-01 |
- create graphs for the each constants.
- All the graphs looks similar to experimental data we had earlier, now to get exact material model we have to compare the values of stress from N1 & N3 values.
- After comparing this we will come to know that the N3 values are more closer to the values of experimental data.
- So N3 model can be selected from that material model.
Simulation:
N1
Effective stress (v-m):
Effective Plastic Strain :
N3
Effective stress (v-m):
Effective Plastic Strain :
RESULT:
1. The Mooney-Rivlin material model is used to define the hyperelastic material represented by a polynomial of order 1. This model is represented as function of strain invariants. This model has two parameters for incompressible model.
2. The Ogden material model is used to define the hyperelastic material represented by multi degree polynomial. This model is represented as a function of principal streches.Ogden model has advantage when it comes to fitting the test curves as parameters are rasied to power which are real number.
3. From our simulation report we can conclude that at poissons ratio 0.495, ogden material model is more accurate to experimental data, so we can use this material model for future reference