Simulating the event of a crash tube crashing onto a rigid wall using the given Radioss starter input file and comparing the results for six different cases by making the necessary modifications.

1. Penalty Method is the most commonly used in explicit codes and can be found in most of the Radioss interfaces.
2. Lagrange Multiplier Method (/LAGMUL and /INTER/LAGMUL) is used in special case studies

(Note that these two are not the only methods used for contact modeling in Radioss. We also have other methods such as Automatic Penalty Lagrange, Hertz Formulation, and ALE Interfaces)

In the penalty method, A gap distance is defined to determine whether or not a node is in contact with a segment. As soon as a node penetrates into the gap, an elastic spring is added between the slave node and the master segment. Therefore, a resistant force will tend to reject the slave node. During the penetration, as a spring is getting connected to the slave node, the spring stiffness must be added to the overall stiffness acting on the node (stiffness from all elements connected to this node). The nodal time step must be reduced to account for the spring stiffness. Contact ends when the penetrated node is completely pushed out of the gap. Therefore, the elastic spring and the reaction forces are removed. It is worthwhile to note that the contact interfaces with the penalty method are fully compatible will all kinematic conditions (for example, a rigid body, imposed velocity, etc.).

Fig 1: The penalty method

In the Lagrange multiplier method, contrary to the penalty method, the Lagrange Multiplier method is purely mathematical and does not require physical elements (springs) to model contact. A nonlinear system of equations is solved to account for contact conditions.

The advantage of the Lagrange multiplier method is that we can prevent the time step collapse that is possible in the penalty method due to high interface stiffness. On the downside, it takes more CPU time to do one cycle as new equations need to be solved by a nonlinear solver.

In this assignment, we will be dealing with only some selected contact types(Type 7 and 11). The list of various contact types(using the penalty method) used in Radioss is shown in Fig 2. Fig 2: List of contact types using the penalty method

Type 7 contact

Interface type 7 is a general-purpose interface and can simulate all types of impact between a set of nodes and a master surface. Interface type 7 solves all problems and limitations encountered with interface types 3 and 5.

Interfaces TYPE3 and TYPE5 have some common problems.

=> Energy jumps

=> Bad contact treatment

=> Limited search algorithm

These common problems are eliminated in Type 7 contacts.

=> In interface type 7, the gap used is on both sides of the shell mid-surface, and a cylindrical gap is added around the edges. This prevents energy jumps as well as keeps the reaction force smooth during sliding between segments.

=> In interface type 7, the stiffness is not constant and increases with the penetration preventing the node from going through the shell mid-surface. This solves many bad contact treatments.

=> It uses a fast search algorithm without limitations.

=> It allows self contact, so preferred in buckling cases as well.

The type 7 interface has some disadvantages as well. The main limitations of this interface are:

=> Time step is reduced in case of high impact speed or contacts with a small gap.

=> It does not work properly if used with a rigid body at high impact speed or rigid body with a small gap.

=> It does not solve edge to edge contact (to solve this, /INTER/TYPE11 should be used along with TYPE7).

The Inacti flag value which we will be changing in case 2 of this assignment decides how the Radioss solver is going to tackle the problem of initial penetrations. An Inacti flag value of 0 will ignore the penetrations while an Inacti value of 5 or 6 will reduce the gap to remove the initial penetrations.

Type 11 contact

The type 11 contact type simulates the impact between edge to Edge or lines. A line can be a beam or truss element or a shell edge or spring elements.

In this type of interface, => Impacts occur between a master and a slave line.

=> A slave line can impact on one or more master lines.

=> A line can belong to the master and the slave side. This allows self-impact.

=> This interface can be used in addition to /INTER/TYPE7 to solve the edge to edge limitation of interface TYPE7.

For more details regarding the contact types, go through the Radioss help document.

PROCEDURE:

1. Case 1:
   1. Import the given Radioss starter input file into Hypermesh and go through the solver deck set up and try to understand.

      Fig 3. The Radioss engine input file

      Fig 3 clearly shows that the analysis run time is set as 30 ms. The animation frequency is kept as 1 ms starting from the beginning of the simulation. The print value of -100 states that the calculated values will be printed once after every 100 values. Tfile value of 0.1 suggests that the values for every 0.1 ms are being recorded in the time history file.

      Fig 4. Property card details in the imported solver deck

      Fig 5. Components defined in the imported solver deck

      Fig 6(a). Boundary conditions(only the translational freedom along the z-axis is allowed)	Fig 6(b). Boundary conditions(an initial velocity of 13.3 m/s is defined in the negative z-axis)

      Fig 7(a). Interface type 7 defined for the self-contact during the crash simulation.	Fig 7(b). Interface type 2 used to define the seam welds tying the components to each other.

   2. Run the analysis without any modification of the imported solver deck using the Radioss panel in the Analysis menu in Hypermesh. (In order to get partwise details of the internal energies, we need to open the solver deck in Hypercrash and create time history for all parts.)
   3. Check for energy error and mass error in the output file after the analysis has been completed. If the errors are within the accepted limits, we can proceed further and generate the required contour animations and plots for Energies and the rigid wall forces.

      Fig 8. Error check(Energy error = -3.8%; mass error = 0% )

   4. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 9. Von-mises stress contour animation

      Fig 10. Time(ms) vs Energy(J) plots

      Fig 11. Time(ms) vs Energy(J) plots for each part

      Fig 12. Time(ms) vs Resultant rigid wall forces(kN) plot

2. Case 2:
   1. Import the given Radioss starter input file into Hypercrash. We need to change the value of the Inacti flag to 6. This can be done using both Hypermesh as well as Hypercrash but Hypercrash being a more user-friendly pre-processor for setting up the solver deck for crash analysis, we will now use Hypercrash to edit the crash analysis set up.

      Fig 13. The imported file in Hypercrash

   2. Create a new time history file recording the values for each part. This will help us understand the changes in internal energy for each part during the simulation runtime.

      Fig 14. The new time history file created to record values for each part separately

   3. Edit the value of Inacti flag to 6.

      Fig 15. The Inacti value changed to 6

      Inacti flag 6 reduces the gap and scales it to 5% to avoid initial penetrations. 0 and 6 are the recommended values for the Inacti flag in crash analysis.

   4. Now that we have made the necessary changes, export the solver deck from Hypercrash and run the analysis in Radioss solver.

      Fig 16. Running the analysis is Radioss

   5. After the run completion, check for the acceptability of the errors. If the energy errors and mass errors are within the limits, then we can proceed for result study and analysis by generating the necessary contours and plots.

      Fig 17. Error check(Energy error = -3.8%; mass error = 0% )

   6. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 17. Von-mises stress contour animation

      Fig 18. Time(ms) vs Energy(J) plots

      Fig 19. Time(ms) vs Energy(J) plots for each part

      Fig 20. Time(ms) vs Resultant rigid wall forces(kN) plot

3. Case 3:
   1. Import the solver deck in Hypercrash.
   2. In case 3, we have to change the interface type to type 11 and then run the analysis. To change the interface type, open the contact interface menu under the Load case tab in Hypercrash. Create a new type 11 interface and enter the recommended parameters. Select the Master segments and slave lines and enable the self contact option.

      Fig 21. Type 11 interface created with recommended parameters

   3. Export the solver deck to the target folder and run the Analysis in Radioss solver.
   4. After the analysis has run successfully, check for energy errors and mass errors in the output file. Similar to the previous cases, see if the errors are within acceptable limits. If yes, then proceed to generate the required plots and contours in Hypergraph and Hyperview respectively.

      Fig 22. Error check(Energy error = -3.8%; mass error = 0% )

   5. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 23. Von-mises stress contour animation

      Fig 24. Time(ms) vs Energy(J) plots

      Fig 25. Time(ms) vs Energy(J) plots for each part

      Fig 26. Time(ms) vs Resultant rigid wall forces(kN) plot

4. Case 4:
   1. Import the starter input file from the case 3 folder into Hypercrash.
   2. Remove the notches by using the align nodes option under the mesh edit panel in Hypercrash. Remove the boundary conditions on the rigid body node.
      

      Fig 27. The crash tube without any notch

   3. Run the analysis using Radioss solver. Once the analysis is completed, check for energy errors and mass errors in the output file. If the errors are thing accepted limits, then proceed to generate the required contour animations and plots.
      

      Fig 28. Error check(Energy error = -2.6%; mass error = 0% )

   4. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 29. Von-mises stress contour animation

      Fig 30. Time(ms) vs Energy(J) plots

      Fig 31. Time(ms) vs Energy(J) plots for each part

      Fig 32. Time(ms) vs Resultant rigid wall forces(kN) plot

5. Case 5:
   1. Import the starter input file from the case 4 folder into Hypercrash.
   2. Create a new notch in the middle portion of the crash tube using the move nodes option under the Mesh edit panel in Hypercrash. Export the solver deck from Hypercrash and run the analysis in Radioss solver.
      

      Fig 33. New notch created in the middle portion

   3. Once the analysis has run successfully, check the errors, and see if they are within the acceptable limits. If so, proceed further and generate the necessary plots and contour animations.

      Fig 34. Error check(Energy error = -3.8%; mass error = 0% )

   4. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 35. Von-mises stress contour animation

      Fig 36. Time(ms) vs Energy(J) plots

      Fig 37. Time(ms) vs Energy(J) plots for each part

      Fig 38. Time(ms) vs Resultant rigid wall forces(kN) plot

6. Case 6:
   1. Import the starter input file from the case 5 folder into Hypercrash.
   2. Modify the notch such that notches are present only on opposing two faces. Export the solver deck from Hypercrash and run the analysis in Radioss solver.

      Fig 39. Modified notch for case 6

   3. Once the analysis has run successfully, check the errors, and see if they are within the acceptable limits. If so, proceed further and generate the necessary plots and contour animations.

      Fig 40. Error check(Energy error = -2.9%; mass error = 0% )

   4. For generating the animations, open the .h3d file from the target folder in the Hyperview window. The plots are generated by importing the time history file in the target folder using Hypergraph.

      Fig 41. Von-mises stress contour animation

      Fig 42. Time(ms) vs Energy(J) plots

      Fig 43. Time(ms) vs Energy(J) plots for each part

      Fig 44. Time(ms) vs Resultant rigid wall forces(kN) plot

RESULTS AND DISCUSSION:

1. Case 1
   1. In case 1, the crash tube has multiple notches and a type 7 contact defined. Fig 45(a) clearly shows that during the impact, the notch regions are the first to deform. The flat regions begin to deform only after the regions below the notches have got completely crushed. The maximum stress was recorded on node 185.
   2. The Internal Energy can be seen to have increased continuously until ~26ms after which, it remained somewhat constant. The increase in Internal energy is accompanied by a similar decrease in Kinetic energy. A possible explanation for this would be the conversion of KE of the crash tube to IE stored while crushing it. The part wise Internal energy plot in fig 45(d) shows the increase in IE of the pshell2_2mm and pshell_2mm until ~10ms, which is when the 2 components having notches got completely crushed. After this point in the simulation, the flat components, ie.PSHELL1 and PSHELL2 begin deforming. At ~16 to ~27ms, the whole crash tube is getting further pressed against the wall. During this period, the increasing contact between the elements has resulted in a jump in the contact energy as observed in fig 45(b). At about 27.5ms, the whole crash tube has gotten crushed and thus no further deformation occurs and the internal energies of the part remain constant after this point.
   3. The time vs Rigidwall forces plot shows a dip every time any part begins to get crushed and once the crushing is over, the forces jump until another part begins to crush. The forces are seen to increase steadily from ~22ms, which is when all the components have gotten crushed and the already crushed crash tube is further pressed against the rigid wall.
   4. The Hourglass energy has stayed zero throughout the simulation due to the choice of recommended shell element formulation.
      

      (a)	(b)

      (c)	(d)
      Fig 45. Case 1 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

2. Case 2
   1. Even though the value for Inacti flag has been changed to 6, no significant changes were observed in case 2. This might be due to the absence of any initial penetrations in the original model.
   2. All the results remained nearly same as in case 1.
      

      (a)	(b)

      (c)	(d)
      Fig 46. Case 2 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

3. Case 3
   1. In spite of adding a type 11 interface, there are no significant changes observed in case 3. However, the maximum vonmisses stress has reduced to 0.692 GPa from 0.698 Gpa in cases 1 and 2.
      

      (a)	(b)

      (c)	(d)
      Fig 47. Case 3 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

4. Case 4
   1. The notches and the boundary conditions have been removed in case 4. In the absence of any notch, the lower part of the crash tube is getting deformed first as a result of the higher stresses experienced there. As the simulation proceeds, we can see the rest of the tube also crushing. The maximum stress was recorded on node 1849.
   2. The plots obtained are similar to those in the previous cases in shape. Fig 49 shows a comparison between the Rigid wall forces plot for cases 3 and 4. Compared to the case 3 plot, a delay of a few microseconds can be observed in case 4 plot. This is because of the shift of the first crushing region from the upper notch in case 3 to the bottom region of the crash tube in case 4.
      

      (a)	(b)

      (c)	(d)
      Fig 48. Case 4 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

      Fig 49. Time vs Rwall forces plot for cases 3 and 4

5. Case 5
   1. In case 5, a notch has been created in the middle portion of the tube. Here, as observed in cases 1,2, and 3, the notch region is the first to deform. Once the deformation starts around the notch regions, the portion below it gets crushed. During this period of crushing, the internal energy of the corresponding parts increases steadily along with the contact energy. After ~10 ms, the upper part of the tube begins to get crushed. The simulation is further proceeding in a manner similar to that observed in case 1.
      

      (a)	(b)

      (c)	(d)
      Fig 50. Case 5 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

6. Case 6
   1. In case 6 the notches are present only on two opposing faces of the crash tube.
   2. Here also, the first deformation is seen in the region around the notch but because it is not a complete notch, the crushing speed is lesser in case 6. While the tube bulges in all four directions in case 5, in case 6, the bulge is only observed on the faces with the notch. This decrease in crushing for case 6 explains why the force plot for case 6 is leading the one for case 5 as shown in fig 52.
   3. The part energy plots, shown in fig 51(d) further showcases the non-similar crushing experienced by the two lower components and the two upper components. This is because of the discontinuous notch.
   4. Otherwise, all the other plots are similar in shape to those in rest of the cases.
      

      (a)	(b)

      (c)	(d)
      Fig 51. Case 6 Results (a)Vonmises stress contour, (b)Time vs Energy plots, (c)Time vs Rwall forces, (d) Time vs IE Plots

      Fig 52. Time vs Rwall forces plot for cases 5 and 6

CONCLUSION:

1. All the cases were successfully simulated after making the necessary modifications.
2. The results were compared and discussed one by one using the various plots and cou=ntour animations generated.
3. It was understood that notches play a significant role in deciding the type of deformation during impact. The notch regions are the first to deform during the event of an impact. Deformation happens in the flat regions only after a significant amount of impact energy has been absorbed during the crushing of the region near to the notches. Thus notches help us have better control on the deformations and force flow.
4. The internal energy plots show a steady increase every time some region is getting crushed. In this way, a lot of Kinetic energy is getting converted into internal energy and contact energy.

Find the simulation file here.

Meshing the bumper assembly:

1. Open the hm file in hypermesh. Only one half of the bumper is present in the imported hm file.
2. Use the auto-mesh panel to create a 2 d shell mesh with Quad elements. Keep the target element size as 6mm.
3. Check the connectivity by pressing shift+f3. Remove the connectivity issues by using the replace node option by pressing the f3 key on keyboard.
4. Now use the reflect option to generate the other half of the Bumper.
5. Use connectors to connect the crash box to the bumper. Here, I have used spot and seam weld connections to assemble the bumper.

   Fig 53. Bumper assembly

Find the completed bumper hm file here.