Assignment4 LuisFigueiredo
Assignment 4
In this assignment, 7 cases will be considered. Each case corresponds to one particular analysis setup. The setups for the analyses are described in the following list:
- Case 1 - Model as it is. Johnson-Cook material with failure specification and failure plastic strain specified
- Case 2 - Similar to Case 1 but with Dadv activated. Johnson-Cook material where the cracks can propagate through the elements
- Case 3 - Johnson-Cook material without failure card.
- Case 4 - Johnson-Cook material without failure card and without failure plastic strain.
- Case 5 - Isotropic linear elastic material
- Case 6 - Brittle material with Ishell = 0
- Case 7 - Brittle material with recommended shell properties
1. Comparison between the analysis
1.1. Total Number of cycles
The total number of cycles was obtained from the .out file that resulted from each analysis.
Case 1 - 49480
Case 2 - 49391
Case 3 - 49405
Case 4 - 48737
Case 5 - 47969
Case 6 - 41208
Case 7 - 49462
1.2. Energy error
The next list displays the maximum error (in absolute value) for each case.
Case 1 - 1.1%
Case 2 - 5.9%
Case 3 - 1.1%
Case 4 - 3.0%
Case 5 - 4.0 %
Case 6 - 7.0 %
Case 7 - 1.2 %
1.3. Mass error
Case 1 - 0.0%
Case 2 - 0.0%
Case 3 - 0.0%
Case 4 - 0.0%
Case 5 - 0.0 %
Case 6 - 0.0 %
Case 7 - 0.0 %
1.4. Simulation time
Case 1 - 79.44 s
Case 2 - 79.54 s
Case 3 - 76.92 s
Case 4 - 80.52 s
Case 5 - 76.71 s
Case 6 - 83.57 s
Case 7 - 84.21 s
2. Comparison between the animations
Case 1 - As expected, the elements are not getting cracked because the propagation of cracks in the mesh occurs either between the elements or by deleting the elements. Also, it was noticed that the maximum value for the plastic strain was 0.151, which corresponds to the established value for the failure plastic strain in the material definition. Also, we can see that the elements that, in one instant, are approaching the strain value of 0.151, are deleted in the next instant.
Case 2 - This case is very simillar to the previous one except that the crack is now able to propagate across the elements, as we can see in the next image. Apart from that, we can still see that some of the elements on the outer edge of the round plate split into two after 4ms of simulation.
Case 3 - In this case, there is an even bigger proximity in terms of results with the first case. The crack does not propagate across the elements and the maximum plastic strain is the same. The biggest difference spotted was the maximum value for the Von Mises stress.
The next images show the difference between case 3 (left) and case 1 (right).
Case 4 - In this case, the failure value for the strain wasn\'t considered. So, that won\'t be a reason for failure of the material.
The results for the maximum deformation are shown in the images below
As we can see in the images above, the maximum Von Mises stress is 425 MPa, which is the maximum value possible for the material, because it follows a stress-strain curve as shown below.
Case 5 - In this case, the material was set to isotropic linear elastic (/LAW1). Since there were no failure cards used, the material didn\'t show any cracks or failures, even if the Von Mises stresses are excessively high, as shown in the next image.
Case 6 - The material card was now set to a law36 type of material, that takes into account the work-hardening part of the stress-strain curve.
The material curve was set as shown in the image below:
Apart from that, the properties of the material were defined as shown in the image below:
The results were the following:
Case 7 - For this case, the material was defined by law27, which corresponds to a brittle material. Its property was updated to Ishell = 24, generating a QEPH type of property, that provides the best balance between accuracy and simulation cost. The results for the last instant of the simulation were the following:
2. Total energy plots
2.1. Case 1
2.2. Case 2
2.3. Case 3
2.4. Case 4
2.5. Case 5
2.6. Case 6
2.7. Case 7
From the graphs displayed above, we can see that the first 3 cases are very simillar, with the exception that the total energy of case 2 stabilizes 0.5 ms later. This might occur because of the energy spent in cracking the elements of the mesh, which makes the total energy of the simulation to stabilize later.
Cases 4 and 5 are also very simillar. This is because neither of the materials on these cases fail, but the main difference lies in the stress-strain curve of each type of material. In case 4, the strain-stress curve is limited in terms of stress, and, in case 5, the stress-strain curve is a straight line passing in the origin, which makes the material on case 5 much stiffer and, therefore, harder to deform, requiring more energy to deform it.
Both cases 6 and 7 define brittle materials. From the animation results, it seemed that the material on case 6 shattered easier that the one on case 7. In the energy plot for case 6 shows zones were the energy increases more drastically. This has to do with the fact that the energy is concentrated quickly in the elements that are almost getting deleted, which makes the energy rise faster, and, once the element is deleted, it stabilizes again. Since the material on case 6 appears to be brittle, these energy \"accumulations\" happen very quickly and to many elements at once, so, the energy plot for case 6 shows a very irregular shape.
3. Conclusions
For this situation, all the cases suggested that the plate should be modelled as an aluminum plate, which is a ductile material. So cases 6 an 7 do not describe the best simulation for this scenario. Also, since there is an imposed movement of the ball against the plate, in a real life scenario, it would be expected to see some kind of failure in the plate, which doesn\'t happen in cases 4 and 5. So these cases also don\'t describe the best approximation for this situation.
Between cases 1,2 and 3; case 2 provided a more accurate vision of what would happen to the plate in a real life scenario, since it showed how the cracks could propagate trough the elements. So, I conclude that the most accurate case is case 2, although the results in this case could have been better if the mesh was more refined, giving an even more detailed idea of how the crack would propagate along the elements.