Week - 10 Hyperelastic Material Models
Hyperelastic Materials
Objective: To calculate Mooney Rivlin and Odgen material constants for the given dog bone specimen.
Hyperelastic Materials: A hyperelastic or Green elastic material is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function.
Mooney Rivlin constant: Mooney Rivlin is a hyperelastic material model, the rubber like material employs strain energy function to enable the determination of stress and displacement. Most use Mooney Rivlin constants to define the material behavior of the model.
Odgen Material: The Ogden material model is a hyperelastic material model used to describe the non-linear stress–strain behaviour of complex materials such as rubbers, polymers, and biological tissue.
Procedure:
- The Dog bone model file is opened in LS-DYNA and viewed in GUI of LS pre-post.
- The appropriate properties of material id, thickness and section id is assigned.
- The given data of engineering Stress and Strain is inputted and saved in the excel file format.
- Using the given data, a curve is defined from *DEFINE key card and the defined curve is assigned to the material cards.
The displacement curve for 100% displacement and stress-strain curve.
- The boundary spc condition and prescribed motion are set accordingly.
The appropriate DATABASE card is assigned to the model.
The appropriate Control cards are assigned to the model.
Case 1: For Hyperelastic Material Model.
N=1
|
Mooney Constant C1 |
0.1768E+00 |
|
Mooney Constant C2 |
0.1474E+00 |
N=2
|
Hyperelastic Constant C10 |
0.2595E+00 |
|
Hyperelastic Constant C01 |
0.4594E-01 |
|
Hyperelastic Constant C11 |
-0.2092E-01 |
|
Hyperelastic Constant C20 |
0.2914E-02 |
|
Hyperelastic Constant C02 |
0.1016E-02 |
|
Hyperelastic Constant C30 |
0.0000E+00 |
For N=3
|
Hyperelastic Constant C10 |
0.2611E+00 |
|
Hyperelastic Constant C01 |
0.4420E-01 |
|
Hyperelastic Constant C11 |
-0.6074E-02 |
|
Hyperelastic Constant C20 |
-0.2667E-02 |
|
Hyperelastic Constant C02 |
-0.9968E-02 |
|
Hyperelastic Constant C30 |
0.1565E-03 |
Case 2: For Odgen Material Model.
N=1
|
mu (1) |
9.107602466133E-01 |
|
alpha (1) |
1.3427238801352E+00 |
N=2
|
mu (1) |
9.1564732574771E-01 |
|
mu (2) |
2.2259557306992E-00 |
|
alpha (1) |
1.3399091914039E+00 |
|
alpha (2) |
1.8434702588141E-03 |
N=3
|
mu (1) |
3.1842578654629E-02 |
|
mu (2) |
2.6137553190073E-01 |
|
mu (3) |
6.8199192356941E-01 |
|
alpha (1) |
1.9263321434400E+00 |
|
alpha (2) |
1.5503405403717E+00 |
|
alpha (3) |
1.2887820953261E+00 |
The simulation for both material properties is carried out.
Conclusion: The given material data is simulated for both the material models [Mooney Rivlin & Odgen]. The data is verified in each material model with different values of N (N1, N2, N3).