Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.
Aim - To perform Tensile test on a solid rubber cube which could be stretched upto 5 times its original length with different element formulations and conclude which of the element formulation could predict real life scenario.
CASE – 1
Elform = 1
Model dimensions = 10X10X10 mm
Case Setup -
Units System considered – gm-mm-ms
Rubber material with properties –
RO = 0.001 gm/mm3
PR = 0.45
Section –
Solid Properties with ELFORM=1
Elform 1 – It is an under integrated constant stress formulation
Which is efficient and accurate. It even works for severe
Deformations but needs hourglass stabilization.
Boundary Conditions-
Units System considered – gm-mm-ms
Displacement applied in –Y
Curve points define from 0 to 45.
As per question Stretch ratio should be considered
Up to 5. Initial dimension = 10 If final dimension is
45+10=55 stretch ratio is greater than 5.
Output Requests -
Control termination – 5 ms
Output Requests –
Database > Binary D3PLOT at DT 1 ms
Database > EXTENT BINARY
Database > ASCII option – GLSTAT, MATSUM AT DT= 1 ms
Result Plot -
Max stress = 2.6165 Mpa
Hourglass Energy -
From the above graph it could be seen that some of the energy was dissipated to overcome hourglass effect.
CASE – 2
Elform = 2
Model dimensions = 10X10X10 mm
Case Setup -
Units System considered – gm-mm-ms
Rubber material with properties –
RO = 0.001 gm/mm3
PR = 0.45
Section –
Solid Properties with ELFORM=2
Elform 2 – It is a fully integrated solid element so no
Hourglass stabilization is needed. But sometimes its too stiff
When aspect ratio is poor (Shear locking)
Boundary Conditions-
Units System considered – gm-mm-ms
Displacement applied in –Y
Curve points define from 0 to 45.
As per question Stretch ratio should be considered
Up to 5. Initial dimension = 10 If final dimension is
45+10=55 stretch ratio is greater than 5.
Output Requests -
Control termination – 5 ms
Output Requests –
Database > Binary D3PLOT at DT 1 ms
Database > EXTENT BINARY
Database > ASCII option – GLSTAT, MATSUM AT DT= 1 ms
Result Plot -
Max stress = 2.942 Mpa
Hourglass Energy -
Since Elform=2 was used which is a fully integrated solid formulation No energy is dissipated to stabilize hourglass
CASE – 3
Elform = -1
Model dimensions = 10X10X10 mm
Case Setup -
Units System considered – gm-mm-ms
Rubber material with properties –
RO = 0.001 gm/mm3
PR = 0.45
Section –
Solid Properties with ELFORM=-1
Elform -1 – It is an efficient formulation which is similar to
Elform=2 except it accounts for poor aspect ratio in order to reduce
Shear locking
Boundary Conditions-
Units System considered – gm-mm-ms
Displacement applied in –Y
Curve points define from 0 to 45.
As per question Stretch ratio should be considered
Up to 5. Initial dimension = 10 If final dimension is
45+10=55 stretch ratio is greater than 5.
Output Requests -
Control termination – 5 ms
Output Requests –
Database > Binary D3PLOT at DT 1 ms
Database > EXTENT BINARY
Database > ASCII option – GLSTAT, MATSUM AT DT= 1 ms
Result Plot -
Max stress = 2.971 Mpa
Hourglass Energy -
Since Elform=-1 was used which is a fully integrated solid formulation No energy is dissipated to stabilize hourglass
CASE – 4
Elform = -2
Model dimensions = 10X10X10 mm
Case Setup -
Units System considered – gm-mm-ms
Rubber material with properties –
RO = 0.001 gm/mm3
PR = 0.45
Section –
Solid Properties with ELFORM=-2
Elform -2 – It is an accurate formulation which is similar to
Elform=2 except it accounts for poor aspect ratio in order to reduce
Shear locking and also is computationally expensive compared to Elform=-1
Boundary Conditions-
Units System considered – gm-mm-ms
Displacement applied in –Y
Curve points define from 0 to 45.
As per question Stretch ratio should be considered
Up to 5. Initial dimension = 10 If final dimension is
45+10=55 stretch ratio is greater than 5.
Output Requests -
Control termination – 5 ms
Output Requests –
Database > Binary D3PLOT at DT 1 ms
Database > EXTENT BINARY
Database > ASCII option – GLSTAT, MATSUM AT DT= 1 ms
Result Plot -
Max stress = 2.956 Mpa
Hourglass Energy -
Since Elform=-2 was used which is a fully integrated solid formulation No energy is dissipated to stabilize hourglass
Post Processing -
Graphs were plotted for Stress vs Time and Strain vs Time Interpolated for 20 Points to get smoother curve.
True stress and True strain data points could be extracted from the graph.
Stretch Ratio is calculated as Exponential of True Strain, Since True Strain = ln(1+Engineering Strain) and 1+Engineering Strain is stretch ratio.
True Stress = Engineering Stress * (1+Engineering Strain)
Therefore, Engineering Stress = True stress/Stretch Ratio
|
Elform = 1 |
|||
|
True Stress |
True Strain |
Stretch Ratio |
Engineering Stress |
|
0.00E+00 |
0.00E+00 |
1 |
0.00E+00 |
|
1.57E-01 |
1.17E-01 |
1.123921226 |
1.40E-01 |
|
3.15E-01 |
2.34E-01 |
1.263198923 |
2.49E-01 |
|
4.72E-01 |
3.50E-01 |
1.419736073 |
3.33E-01 |
|
6.22E-01 |
4.58E-01 |
1.581271505 |
3.93E-01 |
|
7.44E-01 |
5.35E-01 |
1.707743146 |
4.36E-01 |
|
8.67E-01 |
6.12E-01 |
1.844330056 |
4.70E-01 |
|
9.89E-01 |
6.89E-01 |
1.991841436 |
4.97E-01 |
|
1.11E+00 |
7.58E-01 |
2.134354686 |
5.22E-01 |
|
1.24E+00 |
8.16E-01 |
2.261210178 |
5.50E-01 |
|
1.37E+00 |
8.74E-01 |
2.395605333 |
5.73E-01 |
|
1.50E+00 |
9.31E-01 |
2.537988272 |
5.92E-01 |
|
1.62E+00 |
9.78E-01 |
2.658772694 |
6.07E-01 |
|
1.72E+00 |
1.02E+00 |
2.765958944 |
6.21E-01 |
|
1.82E+00 |
1.06E+00 |
2.877465978 |
6.33E-01 |
|
1.92E+00 |
1.10E+00 |
2.993468669 |
6.43E-01 |
|
2.01E+00 |
1.13E+00 |
3.086909546 |
6.52E-01 |
|
2.10E+00 |
1.16E+00 |
3.17731082 |
6.61E-01 |
|
2.19E+00 |
1.18E+00 |
3.270359138 |
6.68E-01 |
|
2.27E+00 |
1.21E+00 |
3.363841501 |
6.75E-01 |
Conclusion -
Region shown in Red box is comparable to the graph on the right. Following the trend Elform=2 reflects similar trend compared to Elform=1,-1 and -2.
