Assignment 4-RADIOSS Material Laws Challenge

AIM: To run a crash analysis on the given Circular FEM model with a Sphere acting as a load, with changes in post-processing the results.

Material Laws Challenges

Objective:

To carry out this simulation of the given starter files and compare the results. There shall be 7 cases and they are to be reached primarily and they are to be compared mainly via animations and plots. The files to be worked on are to be compared mainly via animations and plots.

Cases:

There are 7 no. of Material laws to be followed:

Case 1: Base Simulation with Failure_Johnson_0000.rad for Law 2

Case 2: Failure_Johnson_0000.rad with Ifail_sh = , Dadv = 1, and Ixfem = 1 for Law 2

Case 3: Delete the Johnson Failure card and Run the simulation for Law 2

Case 4: Delete EPS_Max value for Law 2

Case 5: Delete Failure Johnson card and assign the material properties as E, Density, mu.

Case 6: With Shell Properties recommended values which are been used in the videos with Law 27.

Case 7: With Shell Properties recommended values and Load curve with Law 36.

LAW 2:

PLAS_JOHNS) Johnson-cook material- Law 2

• This law represents an isotropic elastoplastic material using the Johnson-cook material model.
• The model expresses material stress as a function of strain, strain rate, and temperature.
• In the material card, we have an option called EPS_max which is nothing but plastic strain at failure. Failure of the element happens when 1 integration point reaches EPS_max.
• Now if failure is only based on EPS_max, there can be instances where the EPS_max gives out unrealistic results. To avoid this, we have the option called /FAILS/JOHN.
• /FAIL/JOHN card provides the user with more control over the failure of the Johnson-cook strain.

LAW36:

PLAS_TAB Elastic-plastic piecewise linear material:

• The LAW36 material law helps in modeling isotropic elastoplastic material using user-defined functions for the work-hardening portion of the stress-strain curve for different strain rates.
• The curve defined is nothing but the stress-strain curve after the yield point. The yield point is set to 0.
• This material law is available for both brick and shell elements.
• If the work hardening portion is defined by the user, then its elastic portion is taken from the inputted Young’s modulus and Poisson’s ratio.
• Any number of stress-strain curves can be defined.
• The important part is that the strain rate curves must not intersect with each other

Case 1:

Open Hypermesh -> Import -> Solver deck option -> Browse File -> Import.

File Name: " FAILURE_JOHNSON_0000.rad is been selected and imported into Hypermesh GUI.

As Shown below:

Check the Failure Card, here we have used Fail Johnson Card for this analysis.

To run this simulation we have to save the output files into new names and check Tools -> Radioss -> Files name -> Options -> Set to -nt 4 -> Hit Radioss.

It is recommended to run the simulation in 4 cores for completion of the simulation early as possible.

"nt" means "number of threads".

once the run is completed we will get an output window, from which we can check whether any errors are been raised or not. Meanwhile check for Errors, warning, Not Include, Does not, and Do not by using "Ctrl + F"

Once after complete the results, we have to click Hyperview as the steps are given below:

• The simulation is complete, now we just need to visualize it. For that, we need to switch to the Hyperview utility.
• After accessing Hyperview, we should input the simulation file. For this, use the h3d file that was generated when RADIOSS processed the starter file. It is generated in the files which are shown in the picture above. After selecting it, we can click 'Apply'
• 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 below

• Then 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 and there is no mass error. Overall, these are very good values.

• Now plot the graphs in Hypergraph 2D. We can switch to it using the same client selector option in the toolbar.
• In the Hypergraph section, we need 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'.

Displacement Plots:

Max of 1.586e+1 mm and Min of 0mm.

Von_Mises_ Stress:

Max of 2.75e+2 N/mm^2 and Min of 0 N/mm^2

Von-Mises Strain:

Max of 1.40e-1 and Min 0 mm/mm.

Plots for Case 1:

I have attached plots for Internal Energy, Kinetic Energy, and Total Energy of 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 many 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 when the elements are deleted, 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.

Total Resultant Forces:

Case 2:

• The process is repeated with slight changes. Just as last time, we import “FAILURE_JOHNSON_0000.rad” via the solver deck.
• This time, we make some changes to the fail/JOHNSON card. It can be accessed via the model tab, under the “Failures” submenu.
• The following values are assigned as shown below (Ifail_sh = 1, Dadv = 1, Ixfem = 1)
• Ifail: 1, which determines the Shell element Failure method. So there are two ways in which we can see the element failing, the element will either get deleted or in some cases, the cracking occurs according to the material properties.
• Ixfem: In this, we can choose that if there is any element that is failing we want that element to delete or we want the element to be cracked. We are going to take Ixfem=1. Which allows failed elements to be cracked not deleted.
• Dadv: It gets activated when we have taken Ixfem=1. We are going to take Dadv=1. Which gives the criteria that how much an element can get broken into small pieces. If it goes beyond the limit the element gets deleted.

Now, after saving all required changes made in it, now we have to run the simulation with the same 4 cores of run power.

After the solver window completes the analysis, as usual, switch to the HyperView window and run the h3d file of the current analysis - Law2_epsmax_crack.h3d and set the Von Mises stress contours, set the Von Mises stress contours, Displacement, and Strain contours are been attached.

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. Set the Von Mises stress contours, Displacement, and Strain contours are been attached.

Displacement Plots:

Max of 1.127e+1 mm and Min of 0mm.

Von-Mises Stress:

Max of 2.951e+2 N/mm^2 and Min of 0 N/mm^2.

Von-Mises Strain:

Max of 1.426e+1 mm/mm and Min of 0mm/mm.

Plots for Case 2:

• In Case 2 we have used 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.
• In this case, the rigid wall is moving. So, to move any object there should be some external force is applying to the object. So that is why the rigid wall forces start increasing from zero and when it collided with the plate, the energy got transferred to the elements, that's the reason the rigid wall forces get decreased again to zero.

Total Resultant Energy:

Case 3:

In this case 3 again, we need to switch to Hyper works and import the solver deck file “Law2_epsmax_crack_0000.rad”, the starter file created in the previous case.

In this case, delete the fail/JOHNSON card. Go to Failures -> Failure_JOHNSON_1.

After deleting the Property of Failure Johnson, then we run the simulation model for "-nt 4", After the solver window completes the analysis, as usual, switch to the HyperView window and run the h3d file of the current analysis - Law2_epsmax_nofail.h3d and set the Von Mises stress contours, Displacement, and Strain contours are been attached.

Failure Johnson has been removed.

The energy error is almost 0 and the mass error is non-existent. Now we can switch to Hypergraph to plot the graphs.

Displacement Plots:

Max of 1.932e+1 mm and Min of 0mm.

Von-Mises Stress:

Max of 6.789e+1 N/mm^2 and Min of 3.107 N/mm^2

Von-Mises Strain:

Max of 1.353e-1 mm/mm and Min of 4.973e-2 mm/mm.

Results for Plots:

• 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 the XFEM crack formulation there.
• There is a linear increase in internal and total energy until the bulk of the elements are deleted from the model. This is expected since the energy absorbed by these elements goes 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

Total Resultant Force:

Case 4:

• In this case, import the case 3 starter file - Law2_epsmax_nofail_0000.rad.
• This time, delete the EPS_p_max value (make it 0). Going to the model tab, we can go to Materials -> Aluminium

Before removal for EPS p max:

After Removal EPS p Max:

The energy error is less than 5% and mass error is non-existent:

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'.

After the solver finishes its analysis, we can switch to Hyperview, run “Law2.h3d”, and activate the Von Mises contours, Displacement plots, and Strain Plots.

Displacement Plots:

Max of 5.011mm and Min of 0mm.

Von-Mises Stress:

Max of 4.247e+2 N/mm^2 and Min of 0 N/mm^2.

Von-Mises Strain:

Max of 3.237e-1 mm/mm and Min of 0 mm/mm.

Results for Plots:

Energies Plots:

• 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 elastoplastic) 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.

Total Resultant Plots:

Case 5:

• In this case, import the main starter file - FAILURE_JOHNSON_0000.rad.
• After that, go to Materials card > Aluminium and change the card image to M1_ELAST, which is Law 1.
• Also set the values for Rho_Initial, E & Nu as follows:
  Rho_initial = 0.0028, E = 71000.00, nu = 0.33.

Material Property:

• Now do the analysis and save the file as “Law1_0000.rad”. Just as before, enable connectors and type '-nt 4' in the options box. Then, we can click radioss and let the solver run the analysis.
• 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:

Displacement Plots:

Max of 5.003 mm and Min of 0mm.

Von-Mises Stress:

Max of 1.089e+4 N/mm^2 and Min of 0 N/mm^2.

Von-Mises Strain:

Max of 1.844e-1 mm/mm and Min of 8.326e-2 mm/mm.

Results for Plots:

Energies Plots:

Total resultant Plots:

Case 6:

• In this case, import the 'LAW27_0000.rad' file.
• We need to use recommended shell properties in this case. Go to Properties > 5NiP. Now, we can 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

Change in properties:

Now, 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.

The energy error is very close to 0 and the mass error is non-existent.

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

Displacement Plots:

Max of 5.023 mm and Min of 0 mm.

Von-Mises Stress:

Max of 4.071e+1 N/mm^2 and Min of 0 N/mm^2.

Von-Mises Strain:

Max of 1.032e-1 mm/mm and Min of 3.811e-2 mm/mm.

Results for Plots:

Energies Plots:

• In this case, the use of the M27_PLAS_BRIT material card is used for the 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.

Total Resultant Plots:

Case 7:

• In this case import 'LAW27_0000.rad' again. We shall be editing certain attributes in this case.
• Go to the model tab and here, we shall be creating a new curve (as per instructions given in the week-4, Materials 7 video). Right-Click >> Create >> Curve
• Initially, there are 4 curves, we are adding the new curve named CASE7.

Now go to Materials >> Aluminium and change the card to M36_PLAS_TAB (Law 36). After that, 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.

Now 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”.

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

Displacement Plots:

Max of 5.825 mm and Min of 0mm.

Von-Mises Stress:

Max of 8.785e+2 N/mm^2 and Min of 0 N/m^2.

Von-Mises Strain:

Max of 1.044e-1 mm/mm and Min of 2.558e-2 mm.

An energy error of -14.8 % 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

Results for Plots:

Energies Plots:

Total Resultant Forces Plots:

Comparison:

The wholes results comparison is shown below:

Learning Outcome:

• Learned about different types of material cards.
• Learn about the failure card in hypermesh.
• Learn about contact energy, hourglass energy, rigid wall forces
• Learned about different simulation results we get using different settings.

Conclusion:

Selecting a correct material model plays a very important role in simulation. Selecting the wrong material model and doing a simulation will also give results but it will not represent the actual situation.

Law 1 is used to model purely elastic materials or materials that remain in the elastic range. To model this we require Poisson's ratio and Young's modulus. This law represents a linear relationship between stress and strain.

Law 2: In this law, the material behaves as linear elastic when the equivalent stress is lower than the yield stress. For a higher value of stress, the material behaves like plastic. Failure can be captured better with the help of an optional Fail_Johnson card.

Law 27: Used for brittle materials.

Law 36: The elastic-plastic behavior of isotropic material is modeled with user-defined functions. The stress-strain curve is modeled using E and Poisson's ratio. Therefore, it is the best card because we cannot know the exact failing condition of the material in the other cases, but we can define the stress-strain curve, and then we can decide where the material is failing.