Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.
OBJECTIVE:
- To create solid block with 10mmx10mmx10mm dimension.
- Simulate tensile test on the model.
- To perform the simulation using ELFORM = 1, 2, -1, -2 by plotting Engineering Stress vs Stretch Ratio up to stretch ratio 5.
PROCEDURE :
Open > Ogden_Material
- Mesh > Shape Mesher > Box Solid
- In Part > Assign Section > Material ID to Ogden_Material.
- In Section > ELFORM as 1
- Boundary Conditions:
- To perform tensile test on solid box with one side along the nodes are fixed along all the axes, except Y & Z.
- Then we fix the vertical middle nodes along all sides except Z.
- Then we fix the horizontal Middle nodes along all directions except Y.
- Prescribed Motion on Nodes opposite to the face of Fixed Nodes
- To achieve a stretch ratio of 5,
True strain (σt)= ln (1+Engg.strain)
Stretch Ratio (λ) = (ΔL/L)
5 = (ΔL/10)
=50
ΔL = 50 mm
- We Define LCID (Load Curve ID) as 50mm.
- The Load curve for dispcement is assigned to the Prescribed Motion Set
Control Cards:
- CONTROL_IMPLICIT_AUTO :
Automatic Time step 0 : Constant Time Step
- CONTROL_IMPLICIT_GENERAL :
IMFLAG is given 1, to Switch Implicit ON
DT0:=Initial time step size for implicit analysis.
- CONTROL_TERMINATION
End time is about 1ms
Database:
- DATABASE_ASCII > GLSTAT & ELOUT.
- DATABASE_BINARY_D3PLOT > DT 0.01
- DATABASE_BINARY_D3PLOT
STRFLG is activated to get strain results
LS-RUN
Engineering stress (σe) = σt / (1+ϵe)
Similarly, True strain (ϵt) = ln(1+ϵe)
Engineering strain (ϵe) = e^ϵt−1
Stretch ratio (λ) = 1+εe
ELEMENT FORMULATION 1 :
| ϵt=ln(1+ϵe) | σt=σe(1+ϵe) | ϵe=exp^(ϵt)−1 | σe=σt/(1+ϵe) | λ=1+εe | σe=σt/(1+ϵe) |
| Tstrain | TStress | Estrain | EStress | Stretch ratio, | EStress |
| 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.00E+00 | 0.00E+00 |
| 4.42E-01 | 5.96E-01 | 5.55E-01 | 3.83E-01 | 1.56E+00 | 1.50E-01 |
| 7.47E-01 | 1.12E+00 | 1.11E+00 | 5.33E-01 | 2.11E+00 | 1.71E-01 |
| 9.81E-01 | 1.64E+00 | 1.67E+00 | 6.14E-01 | 2.67E+00 | 1.67E-01 |
| 1.17E+00 | 2.16E+00 | 2.22E+00 | 6.69E-01 | 3.22E+00 | 1.59E-01 |
| 1.33E+00 | 2.70E+00 | 2.78E+00 | 7.15E-01 | 3.78E+00 | 1.50E-01 |
| 1.47E+00 | 3.27E+00 | 3.33E+00 | 7.54E-01 | 4.33E+00 | 1.41E-01 |
| 1.59E+00 | 3.85E+00 | 3.89E+00 | 7.88E-01 | 4.89E+00 | 1.34E-01 |
| 1.69E+00 | 4.45E+00 | 4.45E+00 | 8.16E-01 | 5.45E+00 | 1.27E-01 |
| 1.79E+00 | 5.02E+00 | 5.00E+00 | 8.37E-01 | 6.00E+00 | 1.20E-01 |
Elform-1 :
| ϵt=ln(1+ϵe) | σt=σe(1+ϵe) | ϵe=exp^(ϵt)−1 | σe=σt/(1+ϵe) | λ=1+εe | σe=σt/(1+ϵe) |
| Tstrain | TStress | Estrain | EStress | Stretch ratio, | EStress |
| 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.00E+00 | 0.00E+00 |
| 4.37E-01 | 5.94E-01 | 5.48E-01 | 3.84E-01 | 1.55E+00 | 1.51E-01 |
| 7.39E-01 | 1.12E+00 | 1.09E+00 | 5.36E-01 | 2.09E+00 | 1.73E-01 |
| 9.75E-01 | 1.64E+00 | 1.65E+00 | 6.17E-01 | 2.65E+00 | 1.69E-01 |
| 1.17E+00 | 2.16E+00 | 2.21E+00 | 6.73E-01 | 3.21E+00 | 1.60E-01 |
| 1.33E+00 | 2.70E+00 | 2.77E+00 | 7.18E-01 | 3.77E+00 | 1.51E-01 |
| 1.46E+00 | 3.27E+00 | 3.31E+00 | 7.58E-01 | 4.31E+00 | 1.43E-01 |
| 1.58E+00 | 3.85E+00 | 3.87E+00 | 7.92E-01 | 4.87E+00 | 1.35E-01 |
| 1.69E+00 | 4.44E+00 | 4.42E+00 | 8.20E-01 | 5.42E+00 | 1.28E-01 |
| 1.79E+00 | 5.02E+00 | 4.97E+00 | 8.40E-01 | 5.97E+00 | 1.20E-01 |
Elform2 :
| ϵt=ln(1+ϵe) | σt=σe(1+ϵe) | ϵe=exp^(ϵt)−1 | σe=σt/(1+ϵe) | λ=1+εe | σe=σt/(1+ϵe) |
| Tstrain | TStress | Estrain | EStress | Stretch ratio, | EStress |
| 0.00E+00 | -2.23E-16 | 0.00E+00 | -2.23E-16 | 1.00E+00 | -1.12E-16 |
| 4.37E-01 | 5.94E-01 | 5.48E-01 | 3.84E-01 | 1.55E+00 | 1.51E-01 |
| 7.39E-01 | 1.12E+00 | 1.09E+00 | 5.36E-01 | 2.09E+00 | 1.73E-01 |
| 9.75E-01 | 1.64E+00 | 1.65E+00 | 6.17E-01 | 2.65E+00 | 1.69E-01 |
| 1.17E+00 | 2.16E+00 | 2.21E+00 | 6.73E-01 | 3.21E+00 | 1.60E-01 |
| 1.33E+00 | 2.70E+00 | 2.76E+00 | 7.17E-01 | 3.76E+00 | 1.51E-01 |
| 1.46E+00 | 3.27E+00 | 3.31E+00 | 7.58E-01 | 4.31E+00 | 1.43E-01 |
| 1.58E+00 | 3.86E+00 | 3.87E+00 | 7.92E-01 | 4.87E+00 | 1.35E-01 |
| 1.69E+00 | 4.44E+00 | 4.42E+00 | 8.20E-01 | 5.42E+00 | 1.28E-01 |
| 1.79E+00 | 5.02E+00 | 4.98E+00 | 8.41E-01 | 5.98E+00 | 1.21E-01 |
Elform-2 :
| ϵt=ln(1+ϵe) | σt=σe(1+ϵe) | ϵe=exp^(ϵt)−1 | σe=σt/(1+ϵe) | λ=1+εe | σe=σt/(1+ϵe) |
| Tstrain | TStress | Estrain | EStress | Stretch ratio, | EStress |
| 0.00E+00 | -2.65E-16 | 0.00E+00 | -2.65E-16 | 1.00E+00 | -1.33E-16 |
| 4.37E-01 | 5.94E-01 | 5.48E-01 | 3.84E-01 | 1.55E+00 | 1.51E-01 |
| 7.39E-01 | 1.12E+00 | 1.09E+00 | 5.36E-01 | 2.09E+00 | 1.73E-01 |
| 9.75E-01 | 1.64E+00 | 1.65E+00 | 6.17E-01 | 2.65E+00 | 1.69E-01 |
| 1.17E+00 | 2.16E+00 | 2.21E+00 | 6.73E-01 | 3.21E+00 | 1.60E-01 |
| 1.33E+00 | 2.70E+00 | 2.76E+00 | 7.17E-01 | 3.76E+00 | 1.51E-01 |
| 1.46E+00 | 3.27E+00 | 3.31E+00 | 7.58E-01 | 4.31E+00 | 1.43E-01 |
| 1.58E+00 | 3.85E+00 | 3.87E+00 | 7.92E-01 | 4.87E+00 | 1.35E-01 |
| 1.69E+00 | 4.44E+00 | 4.42E+00 | 8.20E-01 | 5.42E+00 | 1.28E-01 |
| 1.79E+00 | 5.02E+00 | 4.98E+00 | 8.40E-01 | 5.98E+00 | 1.20E-01 |
Conclusion :
- The Element formulation for the solid cube with tensile test is performed, in which engineering stress & engineering strain datas are calculated and graph plotted for Engineering Stress Vs Strech Ratio
- The Graphs plotted by changing element formulation look alike. The maximum Engineering stress value is 0.173Mpa. The tension test is solved by implicit solver and the analysis is considered to a quasi-static analysis on a hyperelastic non-linear material with slow steady loading conditions.