Assignment 4
Objective : To perform a comparative study on rupture plates by assigning different material properties to the same component and noticing the difference in fracture mechanics.
Procedure :
The results are discussed based on the 5 parameters given in the question above :
1. Total number of cycles, Energy error, mass error and simulation time :
2. The 7 cases are discussed on the basis of animation below:
1.Law2_epsmax_failure :
For this simulation, the elements deform quite a bit plastically after the Yield stress value (290 GPa) is crossed before failing which occurs when the strain crosses the eps_p_max value of 0.151. In this particular case the elements get deleted after they fail and the stress acting on those elements become zero as shown in the picture.
2.Law2_epsmax_crack :
For this simulation, the elements deform quite a bit plastically after the Yield stress value (290 GPa) is crossed before failing which occurs when the strain crosses the eps_p_max value of 0.151. In this particular case the elements get cracked instead of getting deleted after they fail and the stress acting on those elements become zero as shown in the picture. This is because we have activated Dadv and ixfem in the failure card which allows elements to get cracked.
3. Law2_epsmax_nofail :
For this simulation, the elements deform quite a bit plastically after the Yield stress value (290 GPa) is crossed before failing which occurs when the strain crosses the eps_p_max value of 0.151. In this particular case the elements get deleted after they fail and the stress acting on those elements become zero as shown in the picture. This behaviour is similar to the first case Law2_epsmax_failure
4. Law2 :
For this simulation, the elements deform quite a bit plastically after the Yield stress value (290 GPa) is crossed. They however continue to deform untill the maximum stress is being applied but do not fail. This is because we have deleted the value of parameter eps_p_max which is the criteria to fail elements. Hence the elements behave as though they have infinite elasticity.
5. Law1 :
For this simulation, the elements have the law1 card activated in material properties. Due to this they have as though they have infinite elasticity as if the material is in the linear elastic range of Hooke's law. This behaviour is quite similar to Law2 behaviour.
6. Law36 :
For this simulation, the elements deform quite a bit plastically according to the custom function which we have created in the N_func card before failing which occurs when the strain crosses the eps_p_max value of 0.16. In this particular case the elements get deleted after they fail and the stress acting on those elements become zero as shown in the picture.
7. Law27 :
For this simulation, the elements deform very less plastically after the Yield stress value (290 GPa) is crossed before failing which occurs when the strain crosses the eps_t1 value of 0.14.They further follow the path of zero stress at eps_m1 at 0.15 following which they get deleted at eps_f1 of 0.151. As we can see above it behaves as a brittle material formin a very large crack which extends to the circumference of the plate and also breaking further along the circumference due to strain crossing the maximum threshold. This type of behaviour is different from the rest which have varying amounts of elascticity while this type has almost negligible elasticity.
3. Plot of Energies : The total energy. kinetic energy and internal energies are plotted below for each case :
1.Law2_epsmax_failure :
Energy
Stress/Energy
Force
2.Law2_epsmax_crack :
Energy
Energy/stress
Stress/force
3.Law2_epsmax_nofail :
Energy/stress
Energy/stress
Force
4. Law2 :
Energy
Stress
Energy
Force
5. Law1 :
Stress/Energy
Stress/Energy
Force
6. Law36 :
Stress/Energy
Stress/Energy
Force
7. Law27 :
Stress/Energy
Stress/Energy
Force
Observations : For all the above cases the results have been given in table format.
| Max stress | Force | Total Energy | |
| Law2_epsmax_failure | 328.2 Gpa | Increases in zig zag manner until failure and then drops rapidly followed by some deviation until becoming zero. |
Around 28000 Joules |
| Law2_epsmax_crack | 294.7 Gpa | Increases in zig zag manner until failure and then drops irregularly followed by some deviation until becoming zero |
Around 30000 Joules |
| Law2_epsmax_nofail | 270.5 Gpa | Increases in zig zag manner until failure and then drops rapidly followed by some deviation until becoming zero. |
Around 27500 Joules |
| Law2 | 424.7 Gpa | Increases linearly until end of simulation with no drop. | Around 62000 Joules |
| Law1 | 1099 Gpa | Increases very linearly until end of simulation with no drop. | Around 850000 Joules |
| Law36 | 952.1 Gpa | Increases in zig zag manner until failure and then drops rapidly followed by some deviation until becoming zero. |
Around 42000 Joules |
| Law27 | 277.2 Gpa | Increases in zig zag manner until failure and then drops rapidly followed by some deviation until becoming zero. |
Around 41000 Joules |
4. Based on the above simulations, the case that would best represent the onfield scenario would be Law36. Due to the fact that the material behaviour in this case is most accurately represented in the simulation as we have entered the engineering stress strain curve for the material using lab found results and hence the material would behave exactly as how we have observerd, having the realisitc balance of elastic and plastic behaviour. Also, upon observing the simulation we find that the method of failing of elements is most realistic looking at the animations for this simulation.
Also the stress generated in this simulation is quite high and the forces reach a high value before dropping off due to destruction of elements. Hence this result is most accurate amongst the rest.
5. A case by case study has been formulated above on the basis of internal energy, kinetic energy, total energy, normal forces, stresses and given in a descriptive manner.
Observations : In all the cases except Law2 & Law1 we notice that the forces drop by the end of the simulation due to the failure of elements and the energy being dissipated by these elements failing. However in Law1 & Law2 the simulation behaves as though the material has infinte elasticity and as a result the lements do not fail and the forces and stresses have no outlet to dissipate.
This is especially apparent in Law1 as the material behaves fully elastically giving rise to very high stresses of the order of 1099 Gpa, and the force curve not dropping off until the end of the simulation.
In Law2 however even though the material card allows elastic-plastic behaviour, as we have not mentioned the parameter that defines element failure, the element is not allowed to fail and this causes a kind of pseudo-elasticity giving rise to very high stresses of the order of 424.7 Gpa, and the force curve not dropping off until the end of the simulation.
Conclusion : In this way we have studied all the material cards and found out their behaviours for the same simulation in detail.
Result : Google Drive Link