Week - 10 Hyperelastic Material Models
AIM:
To calculate Mooney Rivlin and Odgen's material constants and compare both using stress strain data from a Dogbone Specimen tensile test with 100 percent strain.
PROCEDURE:
1.The given engineering stress-strain values are tabulated and the values are plotted.
2.The given dogbone model is imported.
3.The boundary conditions are assigned.
4.The translation along the Y-axis is only arrested. This is done to achieve realistic deformation on the model.
5.The other end of nodes a boundary prescribed motion set is defined to apply the displacement.
The displacement curve:
6.The scale factor for the displacement definition is given as 100mm. Which is 100 percent strain is equals to a stretch ratio of 2.
λ = 1 + εe
where,
λ = the stretch ratio
εe = the engineering strain
εt = ln(1+εe)
where,
εt = the true strain
2 = 1+Engineering strain which implies Engineering strain = 1
Displacement = ln(2)*145 = 100mm.
7.The material curve ID for the two materials is assigned.
8.The material card for both the materials is assigned.
9.The SECTION_SHELL card is defined with a thickness of 1.5mm. The section and materials cards are assigned to the part card.
10.The CONTROL_IMPLICT card is defined since this analysis can be considered as a static structural problem. The termination time is given as 1ms.
11.The model is saved with .k extension.
OUTPUT AND COMPARRSION:
CASE-1(Mooney-Rivlin Constants):
1.Stress Contours:
For N1:
For N2:
For N3:
The constant values are obtained for N =1,2,3 are
| Hyperelastic N=1 | |||
| Mooney constant c1 = 0.1768E+00 | |||
| Mooney constant c2 = 0.1474E+00 | |||
| Hyperelastic N=2 | |||
| Hyperelastic Constant C10= 0.2595E+00 | |||
| Hyperelastic Constant C01= 0.4594E-01 | |||
| Hyperelastic Constant C11= -0.2092E-01 | |||
| Hyperelastic Constant C20= 0.2913E-02 | |||
| Hyperelastic Constant C02= 0.1016E-02 | |||
| Hyperelastic Constant C30= 0.0000E+00 | |||
| Hyperelastic N=3 | |||
| Hyperelastic Constant C10= 0.2611E+00 | |||
| Hyperelastic Constant C01= 0.4420E-01 | |||
| Hyperelastic Constant C11= -0.6076E-02 | |||
| Hyperelastic Constant C20= -0.2667E-02 | |||
| Hyperelastic Constant C02= -0.9966E-02 | |||
| Hyperelastic Constant C30= 0.1565E-03 | |||
1.The values of true stress and strain are obtained and they are converted to the engineering stress and strain to compare with the experimental data.
Validation Of Constants Obtained:
The material card N is kept as 0 and the obtained constants are plugged in and the model is simulated. For N=1 constant validation procedure is detailed.
The obtained values are tabluated in excel sheet for all three cases and results are compared with experimenatal data.
Case-2 (Ogden Rubber):
Stress contours:
For N=1:
For N=2:
For N=3:
2.The constant values are obtained for N = 1,2,3.
| Ogden N=1 |
| mu(1)= 9.1076025585232E-01 alpha(1)= 1.3427238694706E+00 |
| Ogden N=2 |
| mu(1)= 9.1564733498464E-01 alpha(1)= 1.3399091807896E+00 |
| mu(2)= 2.2259556593837E+00 alpha(2)=-1.8434703015661E-03 |
| Ogden N=3 |
| mu(1)=-3.1842608038997E-02 alpha(1)= 1.9263175501595E+00 |
| mu(2)= 2.6137537530451E-01 alpha(2)= 1.5503338135517E+00 |
| mu(3)= 6.8199188165234E-01 alpha(3)= 1.2887845124363E+00 |
3.The values of true stress and strain are obtained and they are converted to the engineering stress and strain to compare with experimental data.
Validation Of Constants Obtained:
In the material card N is kept as 0 and the obtained constants are plugged in and the model is simulated. For n = 1 constant validation procedure is detailed.
The obtained values are tabulated in excel sheet for all the three cases and results are compared with experimental data.
RESULT:
Thus the Mooney Rivlin and Odgen's material constants and compare both using stress strain data from a Dogbone Specimen tensile test with 100 percent strain is performed sucessfully.