Crashworthiness Analysis using HyperMesh and Radioss Assignment 4-RADIOSS Material Laws Challenge

OBJECTIVE

To carry out simulations of the given starter files and compare the results. There shall be 7 cases (according to given parameters) and they are to be compared primarily via animations and plots. The files to be worked on are the FAILURE_JOHNSON_0000.rad file and the LAW27_0000.rad file. The cases are as follows:

1. Law 2 (file: FAILURE_JOHNSON_0000.rad) - base simulation.
2. Law 2 (file: FAILURE_JOHNSON_0000.rad) with Ifail_sh = 1, Dadv = 1, and Ixfem = 1.
3. Law 2 (file: starter file for case 2) with fail/JOHNSON card deleted.
4. Law 2 (file: starter file for case 3) with EPS_p_max value deleted
5. Law 1 (file: FAILURE_JOHNSON_0000.rad) with fail/JOHNSON card deleted and values for density, E, nu assigned
6. Law 27 (file: LAW27_0000.rad) with recommended shell properties
7. Law 36 (file: LAW27_0000.rad) with recommended shell properties and given reference curve.
   
   

THE MODEL

The simulation will be that of a sphere that rupturing an aluminium plate.

CASE SETUP AND EXECUTION

CASE 1

1. With Hyperworks open, the file is imported via the 'import solver deck' option through File > Import. The 'FAILURE_JOHNSON_0000.rad' file is selected and 'import' is clicked.

2. For this case, we are to run the simulation as is. The file has the following material and failure cards:

To run the simulation, we go to Analysis > Radioss from the bottom panel. We then need to save the file. The file is saved as 'Law2_epsmax_failure_0000.rad'. After saving, we can go ahead and check the 'include connectors' box and type in '-nt 4' in the options text box, before clicking 'Radioss'.

On clicking 'Radioss', we get the solver window, which basically tells us what the RADIOSS solver is doing. After a few minutes, it lets us know that the file has been processed.

3. Once the simulation is complete, now we just need to visualize it. For that, we need to switch to the Hyperview utility. This can be done by clicking the client selector option in the toolbar (might need to be activated from View > Toolbars > Hyperworks > Client Selector). In that menu, we can select Hyperview to switch to it.

After accessing Hyperview, we are asked to input the simulation file. For this, we shall be using the h3d file that was generated when RADIOSS processed the starter file (Law2_epsmax_failure.h3d). It should be generated in the same folder. After selecting it, we can click 'apply'. Doing so generates the simulation animation. We can change what is being represented by selecting the 'contour' option in the toolbar. In this case, we can change the result type to 'Von Mises' and change the averaging method to simple. Doing so creates the Von Mises stress contours as shown:

4. Next step is to carry out energy error and mass error checks and this is done by analyzing the RADIOSS engine output file. This can be accessed from the same directory as the starter and engine files and is denoted by the '.out' extension. We need to check the file that contains '_0001.out' by using any text editor.

On opening the file and scrolling down to the end, we can see the final energy and mass error values.

The final energy error is 0.8%, which is very acceptable. The closer to 0 it is, the better. Added, there is no mass error. Overall, these are very good values.

5. Now we can plot the graphs. For this, we shall be using the Hypergraph client. We can switch to it using the same client selector option in the toolbar.

In the Hypergraph section, we are met with a graph and in the panel below, we are to input a file. For this, we will be using the result file generated by the RADIOSS solver (also known as the 'T01 file'). This file is available in the same directory as the starter, engine and animation files. The file name ends with 'T01'.

After adding it, we can select the variables that would go with time (x-axis).

We shall be looking at and analyzing the graphs in the next section.

CASE 2

1. The process is repeated with slight changes. Just as last time, we import 'FAILURE_JOHNSON_0000.rad' via the solver deck import process.

2. This time, we make some changes to the fail/JOHNSON card. It can be accessed via the model tab, under the 'Failures' submenu.

On clicking Failure_JOHNSON_1, we can edit attributes of the card in the entity editor window in the bottom left. We are looking for the Ifail_sh, Dadv, and Ixfem attributes in particular.

The following values are assigned:
Ifail_sh = 1, Dadv = 1, and Ixfem = 1

3. After the values are changed, we continue as in the previous case by letting the RADIOSS engine run the analysis. This is done via Analysis > Radioss. This time, the file is saved as 'Law2_epsmax_crack_0000.rad'. With connectors checked and '-nt 4' typed in the options box, we can click the Radioss button to run the analysis.

4. After the solver window completes the analysis, as usual, we can switch to the Hyperview window where we run the h3d file of the current analysis - Law2_epsmax_crack.h3d and set the Von Mises stress contours:

5. After that, we can go ahead and check the energy and mass error on the RADIOSS output file,



The energy error is decent enough and is lesser than 5% and mass error is non-existent. We can go ahead and switch to Hypergraph to plot the graphs.


CASE 3

1. Again, we need to switch to Hyperworks and import the solver deck file for this case and that would be Law2_epsmax_crack_0000.rad, the starter file created in the previous case.

2. As we did in the previous case, we need to make changes to this file as well. We need to switch to the model tab and this time, we will be deleting the fail/JOHNSON card altogether. To do that, we can go to Failures > Failure_JOHNSON_1. Right-click Failure_JOHNSON_1 and select 'delete'.

3. After deleting, we are to run the RADIOSS analysis as we did in previous cases through Analysis > Radioss. We can save the file as 'Law2_epsmax_nofail_0000.rad', enable connectors, type '-nt 4' in the options box and click 'Radioss' to run the analysis. After the Radioss solver is complete, we can switch to Hyperview.

4. On Hyperview, we can load the h3d file (Law2_epsmax_nofail.h3d) and click 'apply'. We can then enable the Von Mises contouring and view the simulation.

5. Then, we can carry out the energy and mass error checks:

The energy error is very close to 0 and the mass error is non-existent. Now we can switch to Hypergraph to plot the graphs. They shall be analyzed in the next section.

CASE 4

1. We can switch back to Hyperworks and work on the next case. We shall import the case 3 starter file - Law2_epsmax_nofail_0000.rad.

2. This time, we are to delete the EPS_p_max value. Going to the model tab, we can go to Materials > Aluminium. In the entity editor window, we can clear the EPS_p_max value.

3. After that, we can switch to the Radioss analysis section via Analysis > Radioss, save the file as 'Law2_0000.rad', enable connectors and type in '-nt 4' in the options section and run the analysis by clicking 'Radioss'.

4. After the solver finishes its analysis, we can switch to Hyperview, run 'Law2.h3d', activate the Von Mises contours and view the simulation:

5. After that, we can check the energy and mass errors on 'Law2_0001.out':

The energy error is less than 5% and mass error is non-existent. We can now switch to Hypergraph to plot the graphs for this simulation.

CASE 5

1. We repeat the process again but this time, we import the main starter file - FAILURE_JOHNSON_0000.rad. As in case 2, we can delete the fail/JOHNSON card via the model tab.

2. After that, we can move to Materials > Aluminium. In the entity editor window, we can change the card image to M1_ELAST, which is Law 1.

After doing that, we can set the values for Rho_Initial, E & Nu as follows:
Rho_initial = 0.0028, E = 71000.00, nu = 0.33.

3. Now we can switch to Analysis > Radioss and save the file as 'Law1_0000.rad'. Just as before, we can enable connectors and type '-nt 4' in the options box. Then, we can click radioss and let the solver run the analysis.

4. After the solver completes the analysis, we can switch to Hyperview, import the 'Law1.h3d' file, enable the Von Mises contours and view the simulation:

5. After that, we can check the energy and mass errors on 'Law1_0001.out':



The energy error is less than 5% and the mass error is non-existent. We can then switch to Hypergraph to plot the graphs for this simulation.

CASE 6

1. Switching back to Hyperworks, we can import the 'LAW27_0000.rad' file for this case.

2. We are to use the recommended shell properties in this case. So we can go to the model tab. There, we need to go to Properties > 5NiP. Now, we can take a look at the utility window and set the following attributes as follows:

I_shell=24, I_smstr=2, I_sh3n=2, N=5, I_thick=1, I_plas=1.

3. After doing so, we can run the analysis via the Radioss tool. This time, we can save the file as 'Law27_0000.rad'. Just as before, we can enable connectors and type '-nt 4' in the options box. Then, we can click radioss and let the solver run the analysis.

4. After it's done, we can generate the simulation via Hyperview with the Von Mises contours enabled as shown:

5. After that, we can check the energy and mass errors on 'Law27_0001.out':

The energy error is very close to 0 and the mass error is non-existent. Now we can switch to Hypergraph to plot the graphs. They shall be analyzed in the next section.

CASE 7

1. Switching back to Hyperworks, we can import 'LAW27_0000.rad' again. We shall be editing certain attributes in this case.

2. Go to the model tab and here, we shall be creating a new curve (as per instructions given in the 'Materials 7' video). Right-Click > Create > Curve



In the next window, we can plot the curve using X & Y values. Before that, we can click 'New' and with the newly created curve selected, input the X, Y data as per the data given in the video.

After the curve is created, we can go to Materials > Aluminium and change the card to M36_PLAS_TAB (Law 36). After doing that, we can set the values for Rho_Initial, E & Nu as follows:
Rho_initial = 0.0027, E = 71000.00, nu = 0.33.

We can then add the curve using the N_funct attribute. We can change its value to 1 and by doing so, it lets us select the reference curve. We shall select the one we just made.

3. Now we can move on and run the analysis using the Radioss tool via Analysis > Radioss. The same process, as in previous cases, is repeated. This time, we shall name the file 'LAW36_0000.rad'.

4. After the analysis is complete, we can switch to Hyperview and import 'LAW36.h3d'. With Von Mises contours enabled, we can view the simulation:




5. Checking the energy and mass errors:

An energy error of -1.1% is very acceptable since it's very close to 0. As usual, the mass error is non-existent. Now we can switch to Hypergraph to plot the graph for this simulation. On Hypergraph, we can select the graph attributes and plot as per our requirements (as enunciated in the first case).

OBSERVATIONS

CASE 1

In this case, it has the Fail/JOHNSON card as well as EPS_p_max value assigned, with Ixfem value as 0. This means that the elements are deleted as soon as they cross the EPS_p_max threshold, which is what we can see in the above simulation.



Internal energy as well as rigid wall forces are reactions to the force generated by the sphere on the sheet. Energy increases linearly until a large number of elements are deleted at around the 4ms threshold. This probably creates some vibrations and that results in a surge of kinetic energy at the same point.

The rigid wall forces fluctuate due to element deletions and when a large chunk of elements are deleted at 4ms, the graph drops, meaning there aren't many elements opposing the force of the sphere. Most of the elements in its path have been deleted at that point.

CASE 2

Case 2 makes use of Ifail_sh, Dadv, and Ixfem as part of the Fail/JOHNSON card. Ixfem is especially important here because it decides the way the elements react. With its value equal to 1 here, it means the elements will crack and fail. Along with Dadv, crack propagation can also be seen here, with elements being deleted only when the crack reaches them. As a result, this is a more realistic depiction.

It can be noticed that in both case 1 and 2, the internal energy graphs are almost similar. They differ when it comes to the timestamp at which they plateau and this is probably due to crack propagation being a big factor in case 2. The instant deletion in case 1 as compared to energy dissipation due to cracks in case 2 creates the difference.

CASE 3

With the Fail/JOHNSON card deleted in this case, the onus is on EPS_p_max to be the factor for element deletion. As we can see in the following screenshot, its value is 0.151, meaning elements will be deleted if the strain on any integration point within said elements reaches 15.1% of the plastic strain. The elements, in this case, fail rapidly when compared to the elements in case 2 due to XFEM crack formulation there.

There is a linear increase in internal and total energy until a bulk of the elements are deleted from the model. This is expected since the energy absorbed by these elements go to waste due to their deletion.

This also explains the sudden drop in rigid wall forces at the same timestamp due to most elements that were in contact with the sphere during collision being deleted. The rigid wall force is basically a measure of the opposing force generated by the metal sheet against the sphere. Fluctuations occur when elements are deleted. When there are no elements to oppose the incoming sphere, there won't be any rigid wall forces.

CASE 4

Law 2 (PLAS_JOHNS) expresses material stress as a function of strain, strain rate and temperature. 

The metal sheet is able to withstand a large amount of stress and avoid element deletion primarily due to the fact that the value for EPS_p_max was deleted. Since it was deleted, RADIOSS assigns it the default value of 10^30. In addition to that, the fail/JOHNSON card was deleted. The material behaves like a pseudo-elastic (also called elasto-plastic) material since it has a very high EPS_p_max threshold and elements cannot be deleted due to no failure cards.

With the value of c (Strain rate coefficient) = 0, there is no strain rate (neither does temperature play a role here). As a result, the stress, in this case, is purely a function of strain generated in the material.

Added, the kinetic energy generated in this case is almost negligible (2.5-4 mJ) compared to the internal (and total) energy here. The total energy increase is almost linear over time.

CASE 5

In this case, the plate is defined with a LAW-1 material which defines the basic properties of elastic material. This model considers only the elastic phase of the material, there is no plasticity involved which results in linear deformation.

This case makes use of the M1_Elast card and as we can see, the metal sheet absorbs the full impact of the sphere. This material law is used to model purely elastic materials. This explains why there are no element deletions nor ruptures. Due to its elasticity, it also is able to absorb an extremely large amount of energy, which explains the peak at the end of the kinetic energy plot below. Absorbing a lot of energy also results in very high stresses - the maximum stress observed on the metal sheet is 10890 MPa, which is a massive value compared to the same in LAW 2.

Also, due to the elastic nature, the internal energy (and rigid wall forces) keep increasing exponentially. The internal energy of the metal sheet increases due to the absorption of the kinetic energy from the impacting sphere and drops down once the plate returns to the original shape.

The kinetic energy gradually increases as the plate is stretched to the maximum limit for the applied load.

CASE 6

Case 6 makes use of the M27_PLAS_BRIT material card that is used for isotropic elastoplastic Johnson-Cook material model with an orthotropic brittle failure model. The sheet (compared to case 7) absorbs more force and resorts to more deformation before the elements are deleted (at around 4ms).

With the loss of energy through deleted elements, we notice the graph plateaus at around the 4 ms mark.

With several elements deleted and none to stop the incoming sphere, the rigid wall force graph drops at the same timestamp of 4ms. The spikes are formed when an element is deleted and is characterized by a trough and crest but with so many elements deleted, the trough is massive at the 4ms mark.

CASE 7

In this case, from the simulation, we can say that this material exhibits strong brittle behaviour. It does not bend as much in response to the applied force and immediately disintegrates. There seems to be not much cracking and the region of element deletion takes the shape of the sphere. Another thing that we can notice is that the stress concentration is localized around the region of impact and these stresses are not dissipated throughout the whole metal plate.

Taking a look at the graphs,

There is an almost linear relation between internal energy and time till past the 3ms mark where a large number of elements get deleted at once. When the elements are deleted, the energy on each element goes to waste, which results in the plateauing of the curve.

On the topic of energy wastage and element deletion, it is more particularly visible in the rigid wall force graph. Each of the spikes is due to an element deletion. The resultant force gradually increases past the same 3ms mark which is when the sheet gives way and lets the sphere through. With not much of the sheet in the way, the rigid wall forces are drastically reduced and that results in that drop at the 3ms mark.
The first drop occurs when the sheet ruptures the first time.





TABULATED COMPARISONS

CONCLUSION

Simulations were carried out with different material card laws using different attributes with the help of Hypermesh. The simulation was recorded via Hyperview and graphs were plotted using Hypergraph. Results were compared and compiled.

Cases 4 and 5 are the least realistic of them all since it cannot be expected of a metal sheet to not fail under such duress, especially considering aluminium has a UTS of around 300 MPa. The stresses reached in these cases were way more than that and yet, it did not fail.

In the end, the best case for an on-field scenario depends on the scenario, i.e, if the brittle material must be studied then Law-27 (Case 6) is the best, whereas, to study an elastic material Law-1 would be suitable.