Assignment 4-RADIOSS Material Laws Challenge

AIM:

To run crash analysis on the given model by applying different materials laws available in Radioss and post-process the results

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.

Theory:

• The accuracy of the simulation depends on the material chosen.
• Choosing the right material and providing the reliable material data in performing a simulation is very important.
• RADIOSS has multiple material properties and wide variety of material library like concrete, foam, rubber, composites etc.,
• Some of the commercially used material laws are:

1. Law 1: Elastic (Isotropic Elasticity)
2. Law 2: Johnson-cook (Isotropic Elasto-plastic)
3. Law 27: Elastic-plastic brittle
4. Law 36: Elastic-plastic tabulated
5. Law 42: Ogden (visco hyperelastic)
6. Law 70: Foam

Isotropic Elasticity - Law 1

• Isotropic means that a material will have the same material properties in all 3 directions. Under isotropic elasticity, RADIOSS provides two types of elasticity.
• Linear elastic: LAW1 elastic
• Hyperelastic: LAW69 Tabulated hyperelastic, LAW82 Ogden
• The RADIOSS elasticity law follows the hook’s law of elasticity i.e a linear relationship between the stress and starin.
• It is available for truss, beam, shell, and solid elements.
• As mentioned earlier, it is exclusively for elastic materials.
• The material stiffness is determined by Young’s modules of elasticity (E) and Poisson’s ratio (n).
• The sheer modulus G is calculated by  $G=\frac{E}{2(1+V)}$

   Limitations:

• Elastic materials cannot be used for large deformation cases such as blow molding etc.,
• In the case of large deformation, law 2 johnson-cook material with high yield can be used.

Isotropic Elasto-Plastic 

• RADIOSS provides various types of elasto-plastic material laws. It has all the material models based on von mises hardening without damage, von mises hardening with ductile damage, von mises with visco-plastic flow.
• Here, we are going to look at Johnson-cook/JOHNS and tabulated piece-wise linear/PLAS_TAB.

(PLAS_JOHNS) Johnson-cook material- Law 2

• This law represents an isotropic elasto-plastic 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 modelling isotropic elasto-plastic 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

                                                                            

• The plastic strain curve should start with 0.
• The user also has option to input yield stress with respect to pressure using fct_Idp.

PROCEDUR:

Case 1:

• Open Hyper mesh, go to >> import >> solver deck option >> browse File > Import. The “FAILURE_JOHNSON_0000.rad” file is selected and “imported” as shown below.

                                                           

                                                                                                  Imported rad file

 

• We can check units using the begin card. Standard units are provided in the link below
• https://www.dynasupport.com/howtos/general/consistent-units
• In this base simulation, we will run the simulation with the default values. Therefore don’t change any values.

                                                                                             

 

           

                                                  Default Values of Properties, Material, and Failures Cards

 

• To run the simulation, Go to Analysis >> Radioss. We need to save the output files in a new folder so that we can access them easily. The file is saved as "Law2_epsmax_failure_0000.rad". After saving, tick the 'include connectors' box and type in '-nt 4' in the options text box as shown below, before clicking 'Radioss'
• It is recommended to be written as "-nt 4" as shown in the image below. This means assigning the task to 4 cores in the system, to perform the simulation faster. It depends upon the process of our computer (it has a quad-core processor, then it should be taken as 4. If the system has an octa-core processor, then it is taken as 8). And "nt" means "number of threads". Then click on "Radioss", in order to run the simulation

                                                             

                                               Destination for saving simulation output files  

                                                                                            

• By clicking 'Radioss', we get the solver window as shown below, which basically tells us what the RADIOSS solver is doing. After a few minutes, radios does the job and you can check all the files in the folder which you have saved as.

                                                   

                                                                    Analysis done successfully

• 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 h3d file that was generated when RADIOSS processed the starter file. It is generated in the files swhich 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

   Von. Stress:-   

                                                 

                                                                   Simulation with default values

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

                                                         

                                                          Engine output file for case 1

                                

• 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'.
• I will show all the graphs at the end where we compare all the simulations.

 

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 crack.We are going to take Ixfem=1. Which allow failed element to cracked not to delete.
• Dadv :It gets activated when we have taken Ixfem=1. We are going to takeDadv=1. Which gives the criteria that how much an element can get break into small pieces. If it goes beyond the limit the element gets delete

                                                                                         

 

• Now run the analysis and the file is saved as “Law2_epsmax_crack_0000.rad”. With connectors ticked and '-nt 4' typed in the options box, we can click the Radioss button to run the analysis.
• After the solver window completes the analysis, as usual, switch to HyperView window and run the h3d file of the current analysis - Law2_epsmax_crack.h3d and set the Von Mises stress contours:

                                                                        

• Now, check the energy and mass error on the RADIOSS output file Law2_epsmax_crack_0001.out
• 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.

   

                                                                  

                                                                               Engine output file for case 2

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.

                                                                             

                                                                                               Deleting Failure Johnson

 

• Now run the analysis and the file is saved as “Law2_epsmax_nofail_0000.rad”. With connectors ticked and '-nt 4' typed in the options box, we can click the Radioss button to run the analysis.
• After the solver window completes the analysis, as usual, switch to HyperView window and run the h3d file of the current analysis - Law2_epsmax_nofail.h3d and set the Von Mises stress contours

                                                                  

• Now, check the energy and mass error on the RADIOSS output file Law2_epsmax_nofail_0001.out
• The energy error is almost 0 and the mass error is non-existent. Now we can switch to Hypergraph to plot the graphs.

                                                         

                                                                                            Engine output file for case 3

 

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 as 0). Going to the model tab, we can go to Materials > Aluminium as shown below

                                    

                                                                        Modifying EPS_p_max in materials

• 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”, activate the Von Mises contours and view the simulation

                                                       

• Now, check the energy and mass errors on “Law2_0001.out”
• The energy error is less than 5% and mass error is non-existent.

                                

                                                                                               Engine output file for case 4

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 Changed to LAW 1

• 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:

                                                            

• Now, check the energy and mass error on the RADIOSS output file 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

                                        

                                                                                                Engine output file for case 5

 

CASE 6

• In this case, import the 'LAW27_0000.rad' file.
• Change Mat Law1 To Law36.

                                                   

                                                                       Recommended Mat36

 

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

                                                                   

• 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.

                                              

                                                                                                 Engine output file for case 6

 

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 MAT 36.

                                     

                                                                                             Creating Curve

 

• 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.

                                        

                                                                                              Card Image of curve which we have created

 

                                                                       

                                                                                             Modifying Properties as required

 

• 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, we can view the simulation.

 

• 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

                                             

                                                                                             Engine output file for case 7

     

OBSERVATION:

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.

 

                                          

 

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.

                                            

 

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

                                   

 

Case 6:

• In this case the 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.

                             

 

• There is an almost linear relation between internal energy and time till past the 3ms mark where many 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.

                          

 

• I have prepared a table that compares all the cases which are shown below.

                      

 

Learning Outcome:

• Learned about different type 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 simulation will also give result 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 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.