Assignment 4-RADIOSS Material Laws Challenge

AIM:

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

OBJECTIVE:

• To carry out simulations for given starter files and compare the results. There are 7 cases (according to given parameters) and they are to be compared

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=E/2(1+V)`

Limitations:

• Elastic materials cannot be used for large deformation cases.
• 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 stressstrain 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 then browse File and Import.

IMPORTED 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. so don’t change any values

MATERIAL PROPERTY

• 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

• 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

SIMULATION RESULT FOR CASE 1

• 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% it is acceptable. It closer to 0 and there is no mass error.

0001.OUT FILE RESULT

• Now plot the graphs in Hypergraph 2D.
• 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'.

GRAPH FOR VARIOUS ENERGY

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” sub menu.
• 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 take Dadv=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

PROPERTY

• 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:

SIMULATION RESULT FOR CASE 2

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

0001.OUT FILE RESULT

• The energy error is lesser than 5% and mass error is 0. We can go ahead and switch to Hypergraph to plot the graphs.

GRAPH FOR VARIOUS ENERGY

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.

PROPERTY

• 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

SIMULATION RESULT FOR CASE 3

• Now, check the energy and mass error on the RADIOSS output file Law2_epsmax_nofail_0001.out

0001.OUT FILE RESULT

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

GRAPH FOR VARIOUS ENERGY

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).

PROPERTY

• 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

SIMULATION RESULT FOR CASE 4

• Now, check the energy and mass errors on “Law2_0001.out”

0001.OUT FILE RESULT

• The energy error is less than 5% and mass error is 0.

GRAPH FOR VARIOUS ENERGY

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 Rho_initial = 0.0028, E = 71000.00, nu = 0.33.

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 then 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:

SIMULATION RESULT FOR CASE 5

• Now check the energy and mass error on the RADIOSS output file Law1_0001.out

0001.OUT FILE RESULT

• The energy error is less than 5% and the mass error is 0. We can then switch to Hypergraph to plot the graphs for this simulation

GRAPH FOR VARIOUS ENERGY

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

PROPERTY

• 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

SIMULATION RESULT FOR CASE 6

• we can check the energy and mass errors on “Law27_0001.out”

0001.OUT FILE RESULT

• The energy error is very close to 0 and the mass error is 0.

GRAPH FOR VARIOUS ENERGY

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. Right-Click → Create → Curve
• There are 4 curves, we are adding the new curve named CASE7.

NEW CURVE CREATED FOR CASE 7

• Now go to Materials →Aluminium and change the card to M36_PLAS_TAB (Law 36) then change values of Rho_initial = 0.0027, E = 71000.00, nu = 0.33.
• We can then add the curve using the N_funct . 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.

PROPERTY

• 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

SIMULATION RESULT FOR CASE 7

• we can check the energy and mass errors on “Law36_0001.out”

0001.OUT FILE RESULT

• An energy error of 3.6% is acceptable since it is less than 5%. As usual, the mass error is 0. Now we can switch to Hypergraph to plot
  the graph for this simulation

GRAPH FOR VARIOUS ENERGY

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 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 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 is increase element deletation happen. The elements are creaked then deleted so results in the of the curve is almost linear.
• On the topic of energy wastage and element deletion, it is more particularly visible in the rigid wall force graph. Due to no element
  deletion. The resultant force gradually increases till the end.

TABLE :

CASE	NO.OF CYCLES	MASS ERROR	FINAL ENERGY ERROR (%)	SOLVER SIMULATION PROCESSING TIME (sec)	CONDITION OF ELEMENTS UNDER EXCESSIVE STRESS
CASE 1 (Law2_espmax_failure)	49380	0	0.8	122.18	Deleted
CASE 2 (Law2_espmax_crack)	49217	0	4.1	127.99	Elements under go crack then deleted
CASE 3 (Law2_espmax_nofail)	49408	0	0.8	114.99	Deleted
CASE 4 (Law2)	48737	0	3.0	114.09	Cannot be deleted
CASE 5 (Law1)	47969	0	1.3	113.97	Cannot be deleted due to elestic card property
CASE 6 (Law27)	49508	0	0.8	115.85	Deleted
CASE 7 (Law3)	42165	0	3.6	97.220	Elements under go crack then deleted

CASE 1	CASE 2	CASE 3	CASE 4

CASE 5	CASE 6	CASE 7

Learning Outcome:

• Learned about different type of material cards and failure card in hypermesh.
• Learn about hourglass energy, rigid wall forces
• Learned about different simulation results by using different settings.

CONCLUSION:

• Selecting material is very important in simulation. Selecting the wrong material 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.